references.bib

@ARTICLE{Neal2012-ev,
  title         = "{MCMC} using {H}amiltonian dynamics",
  author        = "Neal, Radford M",
  abstract      = "Hamiltonian dynamics can be used to produce distant
                   proposals for the Metropolis algorithm, thereby avoiding the
                   slow exploration of the state space that results from the
                   diffusive behaviour of simple random-walk proposals. Though
                   originating in physics, Hamiltonian dynamics can be applied
                   to most problems with continuous state spaces by simply
                   introducing fictitious ``momentum'' variables. A key to its
                   usefulness is that Hamiltonian dynamics preserves volume,
                   and its trajectories can thus be used to define complex
                   mappings without the need to account for a hard-to-compute
                   Jacobian factor - a property that can be exactly maintained
                   even when the dynamics is approximated by discretizing time.
                   In this review, I discuss theoretical and practical aspects
                   of Hamiltonian Monte Carlo, and present some of its
                   variations, including using windows of states for deciding
                   on acceptance or rejection, computing trajectories using
                   fast approximations, tempering during the course of a
                   trajectory to handle isolated modes, and short-cut methods
                   that prevent useless trajectories from taking much
                   computation time.",
  month         =  jun,
  year          =  2012,
  archivePrefix = "arXiv",
  primaryClass  = "stat.CO",
  eprint        = "1206.1901"
}


@ARTICLE{Andrieu2008-yc,
  title    = "A tutorial on adaptive {MCMC}",
  author   = "Andrieu, Christophe and Thoms, Johannes",
  abstract = "We review adaptive Markov chain Monte Carlo algorithms (MCMC) as
              a mean to optimise their performance. Using simple toy examples
              we review their theoretical underpinnings, and in particular show
              why adaptive MCMC algorithms might fail when some fundamental
              properties are not satisfied. This leads to guidelines concerning
              the design of correct algorithms. We then review criteria and the
              useful framework of stochastic approximation, which allows one to
              systematically optimise generally used criteria, but also analyse
              the properties of adaptive MCMC algorithms. We then propose a
              series of novel adaptive algorithms which prove to be robust and
              reliable in practice. These algorithms are applied to artificial
              and high dimensional scenarios, but also to the classic mine
              disaster dataset inference problem.",
  journal  = "Stat. Comput.",
  volume   =  18,
  number   =  4,
  pages    = "343--373",
  month    =  dec,
  year     =  2008
}


@ARTICLE{Betancourt2017-ml,
  title         = "A Conceptual Introduction to {H}amiltonian {M}onte {C}arlo",
  author        = "Betancourt, Michael",
  abstract      = "Hamiltonian Monte Carlo has proven a remarkable empirical
                   success, but only recently have we begun to develop a
                   rigorous understanding of why it performs so well on
                   difficult problems and how it is best applied in practice.
                   Unfortunately, that understanding is confined within the
                   mathematics of differential geometry which has limited its
                   dissemination, especially to the applied communities for
                   which it is particularly important. In this review I provide
                   a comprehensive conceptual account of these theoretical
                   foundations, focusing on developing a principled intuition
                   behind the method and its optimal implementations rather of
                   any exhaustive rigor. Whether a practitioner or a
                   statistician, the dedicated reader will acquire a solid
                   grasp of how Hamiltonian Monte Carlo works, when it
                   succeeds, and, perhaps most importantly, when it fails.",
  month         =  jan,
  year          =  2017,
  archivePrefix = "arXiv",
  primaryClass  = "stat.ME",
  eprint        = "1701.02434"
}


@ARTICLE{Hoffman2014-fl,
  title     = "The {No-U-Turn} sampler: adaptively setting path lengths in
               {H}amiltonian {M}onte {C}arlo",
  author    = "Hoffman, Matthew D and Gelman, Andrew",
  abstract  = "Abstract Hamiltonian Monte Carlo (HMC) is a Markov chain Monte
               Carlo (MCMC) algorithm that avoids the random walk behavior and
               sensitivity to correlated parameters that plague many MCMC
               methods by taking a series of steps informed by first-order
               gradient …",
  journal   = "J. Mach. Learn. Res.",
  publisher = "jmlr.org",
  volume    =  15,
  number    =  1,
  pages     = "1593--1623",
  year      =  2014
}


@ARTICLE{Kiselev2019-bt,
  title    = "Challenges in unsupervised clustering of single-cell {RNA-seq}
              data",
  author   = "Kiselev, Vladimir Yu and Andrews, Tallulah S and Hemberg, Martin",
  abstract = "Single-cell RNA sequencing (scRNA-seq) allows researchers to
              collect large catalogues detailing the transcriptomes of
              individual cells. Unsupervised clustering is of central
              importance for the analysis of these data, as it is used to
              identify putative cell types. However, there are many challenges
              involved. We discuss why clustering is a challenging problem from
              a computational point of view and what aspects of the data make
              it challenging. We also consider the difficulties related to the
              biological interpretation and annotation of the identified
              clusters.",
  journal  = "Nat. Rev. Genet.",
  volume   =  20,
  number   =  5,
  pages    = "273--282",
  month    =  may,
  year     =  2019,
  language = "en"
}

@article{orbanz2012lecture,
  title={Lecture notes on {B}ayesian nonparametrics},
  author={Orbanz, Peter},
  month={May},
  year={2014},
  url={http://www.gatsby.ucl.ac.uk/~porbanz/papers/porbanz_BNP_draft.pdf}
}

@article{blei2003latent,
  title={Latent {D}irichlet allocation},
  author={Blei, David M and Ng, Andrew Y and Jordan, Michael I},
  journal={Journal of Machine Learning Research},
  volume={3},
  pages={993--1022},
  year={2003},
  publisher={JMLR. org}
}


@ARTICLE{Blei2017-yc,
  title     = "Variational Inference: A Review for Statisticians",
  author    = "Blei, David M and Kucukelbir, Alp and McAuliffe, Jon D",
  journal   = "Journal of the American Statistical Association",
  publisher = "Taylor \& Francis",
  volume    =  112,
  number    =  518,
  pages     = "859--877",
  month     =  apr,
  year      =  2017
}


% The entry below contains non-ASCII chars that could not be converted
% to a LaTeX equivalent.
@ARTICLE{Boyd-Graber2017-qk,
  title     = "Applications of topic models",
  author    = "Boyd-Graber, Jordan and Hu, Yuening and Mimno, David",
  abstract  = "How can a single person understand what's going on in a
               collection of millions of documents? This is an increasingly
               common problem: sifting through an organization's e- mails,
               understanding a decade worth of newspapers, or characterizing a
               scientific field's …",
  journal   = "Found. Trends\textregistered{} Inf. Retr.",
  publisher = "Now Publishers",
  volume    =  11,
  number    = "2-3",
  pages     = "143--296",
  year      =  2017,
  language  = "en"
}

@article{blei2012probabilistic,
  title={Probabilistic topic models},
  author={Blei, David M},
  journal={Communications of the ACM},
  volume={55},
  number={4},
  pages={77--84},
  year={2012},
  publisher={ACM New York, NY, USA}
}

@inproceedings{blei2006dynamic,
  title={Dynamic topic models},
  author={Blei, David M and Lafferty, John D},
  booktitle={Proceedings of the 23rd international conference on Machine learning},
  pages={113--120},
  year={2006}
}

@inproceedings{wallach2009evaluation,
  title={Evaluation methods for topic models},
  author={Wallach, Hanna M and Murray, Iain and Salakhutdinov, Ruslan and Mimno, David},
  booktitle={Proceedings of the 26th Annual International Conference on Machine Learning},
  pages={1105--1112},
  year={2009}
}


@ARTICLE{Gopalan2013-bc,
  title         = "Scalable Recommendation with {P}oisson Factorization",
  author        = "Gopalan, Prem and Hofman, Jake M and Blei, David M",
  month         =  nov,
  year          =  2013,
  archivePrefix = "arXiv",
  primaryClass  = "cs.IR",
  eprint        = "1311.1704"
}


@ARTICLE{Gopalan2013-pz,
  title    = "Efficient discovery of overlapping communities in massive
              networks",
  author   = "Gopalan, Prem K and Blei, David M",
  journal  = "Proc. Natl. Acad. Sci. U. S. A.",
  volume   =  110,
  number   =  36,
  pages    = "14534--14539",
  month    =  sep,
  year     =  2013,
  keywords = "Bayesian statistics; massive data; network analysis",
  language = "en"
}

@article{hoffman2013stochastic,
  title={Stochastic variational inference.},
  author={Hoffman, Matthew D and Blei, David M and Wang, Chong and Paisley, John},
  journal={Journal of Machine Learning Research},
  volume={14},
  number={5},
  year={2013}
}

@article{neal2012mcmc,
  title={{MCMC} using {H}amiltonian dynamics},
  author={Neal, Radford M},
  journal={Handbook of Markov Chain Monte Carlo},
  volume={2},
  number={11},
  pages={2},
  year={2011},
  publisher={CRC Press}
}

@article{betancourt2017conceptual,
  title={A conceptual introduction to {H}amiltonian {M}onte {C}arlo},
  author={Betancourt, Michael},
  journal={arXiv preprint arXiv:1701.02434},
  year={2017}
}

@article{hoffman2014nuts,
  title={The {No-U-Turn} sampler: adaptively setting path lengths in {H}amiltonian {M}onte {C}arlo},
  author={Hoffman, Matthew D and Gelman, Andrew},
  journal={Journal of Machine Learning Research},
  volume={15},
  number={1},
  pages={1593--1623},
  year={2014}
}

@article{amari1998natural,
  title={Natural gradient works efficiently in learning},
  author={Amari, Shun-Ichi},
  journal={Neural computation},
  volume={10},
  number={2},
  pages={251--276},
  year={1998},
  publisher={MIT Press}
}


@ARTICLE{Erosheva2007-vd,
  title     = "DESCRIBING DISABILITY THROUGH INDIVIDUAL-LEVEL MIXTURE
               MODELS For MULTIVARIATE BINARY DATA",
  author    = "Erosheva, Elena A and Fienberg, Stephen E and Joutard, Cyrille",
  abstract  = "Data on functional disability are of widespread policy interest
               in the United States, especially with respect to planning for
               Medicare and Social Security for a growing population of elderly
               adults. We consider an extract of functional disability data
               from the National Long Term Care Survey (NLTCS) and attempt to
               develop disability profiles using variations of the Grade of
               Membership (GoM) model. We first describe GoM as an
               individual-level mixture model that allows individuals to have
               partial membership in several mixture components simultaneously.
               We then prove the equivalence between individual-level and
               population-level mixture models, and use this property to
               develop a Markov Chain Monte Carlo algorithm for Bayesian
               estimation of the model. We use our approach to analyze
               functional disability data from the NLTCS.",
  journal   = "Ann. Appl. Stat.",
  publisher = "ncbi.nlm.nih.gov",
  volume    =  1,
  number    =  2,
  pages     = "346--384",
  year      =  2007,
  language  = "en"
}

% The entry below contains non-ASCII chars that could not be converted
% to a LaTeX equivalent.
@ARTICLE{Hofmann1999-de,
  title     = "Probabilistic latent semantic indexing",
  author    = "Hofmann, T",
  abstract  = "Abstract Probabilistic Latent Semantic Indexing is a novel
               approach to automated document indexing which is based on a
               statistical latent class model for factor analysis of count
               data. Fitted from a training corpus of text documents by a
               generalization of the Expectation …",
  journal   = "Proceedings of the 22nd annual international ACM",
  publisher = "dl.acm.org",
  year      =  1999
}

@ARTICLE{Deerwester1990-kp,
  title     = "Indexing by latent semantic analysis",
  author    = "Deerwester, Scott and Dumais, Susan T and Furnas, George W and
               Landauer, Thomas K and Harshman, Richard",
  abstract  = "Abstract A new method for automatic indexing and retrieval is
               described. The approach is to take advantage of implicit
               higher-order structure in the association of terms with
               documents (?semantic structure?) in order to improve the
               detection of relevant documents on the basis of terms found in
               queries. The particular technique used is singular-value
               decomposition, in which a large term by document matrix is
               decomposed into a set of ca. 100 orthogonal factors from which
               the original matrix can be approximated by linear combination.
               Documents are represented by ca. 100 item vectors of factor
               weights. Queries are represented as pseudo-document vectors
               formed from weighted combinations of terms, and documents with
               supra-threshold cosine values are returned. Initial tests find
               this completely automatic method for retrieval to be promising.
               ? 1990 John Wiley \& Sons, Inc.",
  journal   = "J. Am. Soc. Inf. Sci.",
  publisher = "Wiley",
  volume    =  41,
  number    =  6,
  pages     = "391--407",
  month     =  sep,
  year      =  1990,
  language  = "en"
}


@ARTICLE{Pritchard2000-wm,
  title     = "Inference of population structure using multilocus genotype data",
  author    = "Pritchard, J K and Stephens, M and Donnelly, P",
  abstract  = "We describe a model-based clustering method for using multilocus
               genotype data to infer population structure and assign
               individuals to populations. We assume a model in which there are
               K populations (where K may be unknown), each of which is
               characterized by a set of allele frequencies at each locus.
               Individuals in the sample are assigned (probabilistically) to
               populations, or jointly to two or more populations if their
               genotypes indicate that they are admixed. Our model does not
               assume a particular mutation process, and it can be applied to
               most of the commonly used genetic markers, provided that they
               are not closely linked. Applications of our method include
               demonstrating the presence of population structure, assigning
               individuals to populations, studying hybrid zones, and
               identifying migrants and admixed individuals. We show that the
               method can produce highly accurate assignments using modest
               numbers of loci-e.g. , seven microsatellite loci in an example
               using genotype data from an endangered bird species. The
               software used for this article is available from
               http://www.stats.ox.ac.uk/ approximately pritch/home. html.",
  journal   = "Genetics",
  publisher = "academic.oup.com",
  volume    =  155,
  number    =  2,
  pages     = "945--959",
  month     =  jun,
  year      =  2000,
  language  = "en"
}


@ARTICLE{Airoldi2008-rh,
  title    = "Mixed Membership Stochastic Blockmodels",
  author   = "Airoldi, Edoardo M and Blei, David M and Fienberg, Stephen E and
              Xing, Eric P",
  abstract = "Observations consisting of measurements on relationships for
              pairs of objects arise in many settings, such as protein
              interaction and gene regulatory networks, collections of
              author-recipient email, and social networks. Analyzing such data
              with probabilisic models can be delicate because the simple
              exchangeability assumptions underlying many boilerplate models no
              longer hold. In this paper, we describe a latent variable model
              of such data called the mixed membership stochastic blockmodel.
              This model extends blockmodels for relational data to ones which
              capture mixed membership latent relational structure, thus
              providing an object-specific low-dimensional representation. We
              develop a general variational inference algorithm for fast
              approximate posterior inference. We explore applications to
              social and protein interaction networks.",
  journal  = "J. Mach. Learn. Res.",
  volume   =  9,
  pages    = "1981--2014",
  month    =  sep,
  year     =  2008,
  language = "en"
}

@book{bishop2006pattern,
  title={Pattern recognition and machine learning},
  author={Bishop, Christopher M},
  year={2006},
  publisher={Springer}
}

@inproceedings{cremer2018inference,
  title={Inference suboptimality in variational autoencoders},
  author={Cremer, Chris and Li, Xuechen and Duvenaud, David},
  booktitle={International Conference on Machine Learning},
  pages={1078--1086},
  year={2018},
  organization={PMLR}
}

@book{williams1996gaussian,
  title={Gaussian processes for regression},
  author={Williams, Christopher KI and Rasmussen, Carl Edward},
  year={1996},
  publisher={MIT Press}
}


@INPROCEEDINGS{Storkey1999-wq,
  title     = "Truncated covariance matrices and Toeplitz methods in Gaussian
               processes",
  booktitle = "Artificial Neural Networks, 1999. {ICANN} 99. Ninth
               International Conference on (Conf. Publ. No. 470)",
  author    = "Storkey, Amos J",
  abstract  = "Gaussian processes are a limit extension of neural networks.
               Standard Gaussian process techniques use a squared exponential
               covariance function. Here, the use of truncated covariances is
               proposed. Such covariances have compact support. Their use
               speeds up matrix inversion and increases precision. Furthermore
               they allow the use of speedy, memory efficient Toeplitz
               inversion for high dimensional grid based Gaussian process
               predictors",
  publisher = "unknown",
  volume    =  1,
  pages     = "55--60 vol.1",
  month     =  feb,
  year      =  1999
}


@INPROCEEDINGS{Cunningham2008-zj,
  title     = "Fast {G}aussian process methods for point process intensity
               estimation",
  booktitle = "Proceedings of the 25th International Conference on Machine
               Learning",
  author    = "Cunningham, John P and Shenoy, Krishna V and Sahani, Maneesh",
  abstract  = "Point processes are difficult to analyze because they provide
               only a sparse and noisy observation of the intensity function
               driving the process. Gaussian Processes offer an attractive
               framework within which to infer underlying intensity functions.
               The result of this inference is a continuous function defined
               across time that is typically more amenable to analytical
               efforts. However, a naive implementation will become
               computationally infeasible in any problem of reasonable size,
               both in memory and run time requirements. We demonstrate problem
               specific methods for a class of renewal processes that eliminate
               the memory burden and reduce the solve time by orders of
               magnitude.",
  publisher = "Association for Computing Machinery",
  pages     = "192--199",
  month     =  jul,
  year      =  2008,
  address   = "New York, NY, USA",
  location  = "Helsinki, Finland"
}

@inproceedings{duvenaud2013structure,
  title={Structure discovery in nonparametric regression through compositional kernel search},
  author={Duvenaud, David and Lloyd, James and Grosse, Roger and Tenenbaum, Joshua and Zoubin, Ghahramani},
  booktitle={International Conference on Machine Learning},
  pages={1166--1174},
  year={2013},
  organization={PMLR}
}


@ARTICLE{Neal2003-zu,
  title     = "Slice sampling",
  author    = "Neal, Radford M",
  abstract  = "Markov chain sampling methods that adapt to characteristics of
               the distribution being sampled can be constructed using the
               principle that one can ample from a distribution by sampling
               uniformly from the region under the plot of its density
               function. A Markov chain that converges to this uniform
               distribution can be constructed by alternating uniform sampling
               in the vertical direction with uniform sampling from the
               horizontal ``slice'' defined by the current vertical position,
               or more generally, with some update that leaves the uniform
               distribution over this slice invariant. Such ``slice sampling''
               methods are easily implemented for univariate distributions, and
               can be used to sample from a multivariate distribution by
               updating each variable in turn. This approach is often easier to
               implement than Gibbs sampling and more efficient than simple
               Metropolis updates, due to the ability of slice sampling to
               adaptively choose the magnitude of changes made. It is therefore
               attractive for routine and automated use. Slice sampling methods
               that update all variables simultaneously are also possible.
               These methods can adaptively choose the magnitudes of changes
               made to each variable, based on the local properties of the
               density function. More ambitiously, such methods could
               potentially adapt to the dependencies between variables by
               constructing local quadratic approximations. Another approach is
               to improve sampling efficiency by suppressing random walks. This
               can be done for univariate slice sampling by ``overrelaxation,''
               and for multivariate slice sampling by ``reflection'' from the
               edges of the slice.",
  journal   = "Annals of Statistics",
  publisher = "Institute of Mathematical Statistics",
  volume    =  31,
  number    =  3,
  pages     = "705--767",
  month     =  jun,
  year      =  2003,
  keywords  = "65C05; 65C60; Adaptive methods; auxiliary variables; dynamical
               methods; Gibbs sampling; Markov chain Monte Carlo; Metropolis
               algorithm; overrelaxation;",
  language  = "en"
}


@INPROCEEDINGS{Murray2010-zb,
  title      = "Elliptical slice sampling",
  booktitle  = "Proceedings of the Thirteenth International Conference on
                Artificial Intelligence and Statistics",
  author     = "Murray, Iain and Adams, Ryan and MacKay, David",
  abstract   = "Many probabilistic models introduce strong dependencies between
                variables using a latent multivariate Gaussian distribution or
                a Gaussian process. We present a new Markov chain Monte Carlo
                algorithm for performing inference in models with multivariate
                Gaussian priors. Its key properties are: 1) it has simple,
                generic code applicable to many models, 2) it has no free
                parameters, 3) it works well for a variety of Gaussian process
                based models. These properties make our method ideal for use
                while model building, removing the need to spend time deriving
                and tuning updates for more complex algorithms.",
  publisher  = "jmlr.org",
  pages      = "541--548",
  month      =  mar,
  year       =  2010,
  language   = "en",
  conference = "Proceedings of the Thirteenth International Conference on
                Artificial Intelligence and Statistics"
}


@INPROCEEDINGS{Hensman2013-cf,
  title     = "Gaussian processes for Big data",
  booktitle = "Proceedings of the {Twenty-Ninth} Conference on Uncertainty in
               Artificial Intelligence",
  author    = "Hensman, James and Fusi, Nicol{\`o} and Lawrence, Neil D",
  abstract  = "We introduce stochastic variational inference for Gaussian
               process models. This enables the application of Gaussian process
               (GP) models to data sets containing millions of data points. We
               show how GPs can be variationally decomposed to depend on a set
               of globally relevant inducing variables which factorize the
               model in the necessary manner to perform variational inference.
               Our approach is readily extended to models with non-Gaussian
               likelihoods and latent variable models based around Gaussian
               processes. We demonstrate the approach on a simple toy problem
               and two real world data sets.",
  publisher = "AUAI Press",
  pages     = "282--290",
  series    = "UAI'13",
  month     =  aug,
  year      =  2013,
  address   = "Arlington, Virginia, USA",
  location  = "Bellevue, WA"
}


@INPROCEEDINGS{Titsias2009-ls,
  title     = "Variational Learning of Inducing Variables in Sparse Gaussian
               Processes",
  booktitle = "Proceedings of the Twelth International Conference on Artificial
               Intelligence and Statistics",
  author    = "Titsias, Michalis",
  editor    = "van Dyk, David and Welling, Max",
  abstract  = "Sparse Gaussian process methods that use inducing variables
               require the selection of the inducing inputs and the kernel
               hyperparameters. We introduce a variational formulation for
               sparse approximations that jointly infers the inducing inputs
               and the kernel hyperparameters by maximizing a lower bound of
               the true log marginal likelihood. The key property of this
               formulation is that the inducing inputs are defined to be
               variational parameters which are selected by minimizing the
               Kullback-Leibler divergence between the variational distribution
               and the exact posterior distribution over the latent function
               values. We apply this technique to regression and we compare it
               with other approaches in the literature.",
  publisher = "PMLR",
  volume    =  5,
  pages     = "567--574",
  series    = "Proceedings of Machine Learning Research",
  year      =  2009,
  address   = "Hilton Clearwater Beach Resort, Clearwater Beach, Florida USA"
}


@ARTICLE{Miller2018-dv,
  title    = "Mixture models with a prior on the number of components",
  author   = "Miller, Jeffrey W and Harrison, Matthew T",
  abstract = "A natural Bayesian approach for mixture models with an unknown
              number of components is to take the usual finite mixture model
              with symmetric Dirichlet weights, and put a prior on the number
              of components-that is, to use a mixture of finite mixtures (MFM).
              The most commonly-used method of inference for MFMs is reversible
              jump Markov chain Monte Carlo, but it can be nontrivial to design
              good reversible jump moves, especially in high-dimensional
              spaces. Meanwhile, there are samplers for Dirichlet process
              mixture (DPM) models that are relatively simple and are easily
              adapted to new applications. It turns out that, in fact, many of
              the essential properties of DPMs are also exhibited by MFMs-an
              exchangeable partition distribution, restaurant process, random
              measure representation, and stick-breaking representation-and
              crucially, the MFM analogues are simple enough that they can be
              used much like the corresponding DPM properties. Consequently,
              many of the powerful methods developed for inference in DPMs can
              be directly applied to MFMs as well; this simplifies the
              implementation of MFMs and can substantially improve mixing. We
              illustrate with real and simulated data, including
              high-dimensional gene expression data used to discriminate cancer
              subtypes.",
  journal  = "J. Am. Stat. Assoc.",
  volume   =  113,
  number   =  521,
  pages    = "340--356",
  year     =  2018,
  keywords = "Bayesian; clustering; density estimation; model selection;
              nonparametric",
  language = "en"
}

@book{neal1996bayesian,
  title={Bayesian learning for neural networks},
  author={Neal, Radford M},
  year={1996},
  publisher={Springer Science \& Business Media}
}


@ARTICLE{Jacot2018-dl,
  title         = "Neural Tangent Kernel: Convergence and Generalization in
                   Neural Networks",
  author        = "Jacot, Arthur and Gabriel, Franck and Hongler, Cl{\'e}ment",
  abstract      = "At initialization, artificial neural networks (ANNs) are
                   equivalent to Gaussian processes in the infinite-width
                   limit, thus connecting them to kernel methods. We prove that
                   the evolution of an ANN during training can also be
                   described by a kernel: during gradient descent on the
                   parameters of an ANN, the network function $f_\theta$ (which
                   maps input vectors to output vectors) follows the kernel
                   gradient of the functional cost (which is convex, in
                   contrast to the parameter cost) w.r.t. a new kernel: the
                   Neural Tangent Kernel (NTK). This kernel is central to
                   describe the generalization features of ANNs. While the NTK
                   is random at initialization and varies during training, in
                   the infinite-width limit it converges to an explicit
                   limiting kernel and it stays constant during training. This
                   makes it possible to study the training of ANNs in function
                   space instead of parameter space. Convergence of the
                   training can then be related to the positive-definiteness of
                   the limiting NTK. We prove the positive-definiteness of the
                   limiting NTK when the data is supported on the sphere and
                   the non-linearity is non-polynomial. We then focus on the
                   setting of least-squares regression and show that in the
                   infinite-width limit, the network function $f_\theta$
                   follows a linear differential equation during training. The
                   convergence is fastest along the largest kernel principal
                   components of the input data with respect to the NTK, hence
                   suggesting a theoretical motivation for early stopping.
                   Finally we study the NTK numerically, observe its behavior
                   for wide networks, and compare it to the infinite-width
                   limit.",
  month         =  jun,
  year          =  2018,
  archivePrefix = "arXiv",
  primaryClass  = "cs.LG",
  eprint        = "1806.07572"
}

@ARTICLE{Arora2019-uc,
  title         = "On Exact Computation with an Infinitely Wide Neural Net",
  author        = "Arora, Sanjeev and Du, Simon S and Hu, Wei and Li, Zhiyuan
                   and Salakhutdinov, Ruslan and Wang, Ruosong",
  abstract      = "How well does a classic deep net architecture like AlexNet
                   or VGG19 classify on a standard dataset such as CIFAR-10
                   when its width --- namely, number of channels in
                   convolutional layers, and number of nodes in fully-connected
                   internal layers --- is allowed to increase to infinity? Such
                   questions have come to the forefront in the quest to
                   theoretically understand deep learning and its mysteries
                   about optimization and generalization. They also connect
                   deep learning to notions such as Gaussian processes and
                   kernels. A recent paper [Jacot et al., 2018] introduced the
                   Neural Tangent Kernel (NTK) which captures the behavior of
                   fully-connected deep nets in the infinite width limit
                   trained by gradient descent; this object was implicit in
                   some other recent papers. An attraction of such ideas is
                   that a pure kernel-based method is used to capture the power
                   of a fully-trained deep net of infinite width. The current
                   paper gives the first efficient exact algorithm for
                   computing the extension of NTK to convolutional neural nets,
                   which we call Convolutional NTK (CNTK), as well as an
                   efficient GPU implementation of this algorithm. This results
                   in a significant new benchmark for the performance of a pure
                   kernel-based method on CIFAR-10, being $10\%$ higher than
                   the methods reported in [Novak et al., 2019], and only $6\%$
                   lower than the performance of the corresponding finite deep
                   net architecture (once batch normalization, etc. are turned
                   off). Theoretically, we also give the first non-asymptotic
                   proof showing that a fully-trained sufficiently wide net is
                   indeed equivalent to the kernel regression predictor using
                   NTK.",
  month         =  apr,
  year          =  2019,
  archivePrefix = "arXiv",
  primaryClass  = "cs.LG",
  eprint        = "1904.11955"
}

@ARTICLE{Yang2019-uu,
  title         = "Scaling Limits of Wide Neural Networks with Weight Sharing:
                   Gaussian Process Behavior, Gradient Independence, and Neural
                   Tangent Kernel Derivation",
  author        = "Yang, Greg",
  abstract      = "Several recent trends in machine learning theory and
                   practice, from the design of state-of-the-art Gaussian
                   Process to the convergence analysis of deep neural nets
                   (DNNs) under stochastic gradient descent (SGD), have found
                   it fruitful to study wide random neural networks. Central to
                   these approaches are certain scaling limits of such
                   networks. We unify these results by introducing a notion of
                   a straightline \textbackslashemph\{tensor program\} that can
                   express most neural network computations, and we
                   characterize its scaling limit when its tensors are large
                   and randomized. From our framework follows (1) the
                   convergence of random neural networks to Gaussian processes
                   for architectures such as recurrent neural networks,
                   convolutional neural networks, residual networks, attention,
                   and any combination thereof, with or without batch
                   normalization; (2) conditions under which the
                   \textbackslashemph\{gradient independence assumption\} --
                   that weights in backpropagation can be assumed to be
                   independent from weights in the forward pass -- leads to
                   correct computation of gradient dynamics, and corrections
                   when it does not; (3) the convergence of the Neural Tangent
                   Kernel, a recently proposed kernel used to predict training
                   dynamics of neural networks under gradient descent, at
                   initialization for all architectures in (1) without batch
                   normalization. Mathematically, our framework is general
                   enough to rederive classical random matrix results such as
                   the semicircle and the Marchenko-Pastur laws, as well as
                   recent results in neural network Jacobian singular values.
                   We hope our work opens a way toward design of even stronger
                   Gaussian Processes, initialization schemes to avoid gradient
                   explosion/vanishing, and deeper understanding of SGD
                   dynamics in modern architectures.",
  month         =  feb,
  year          =  2019,
  archivePrefix = "arXiv",
  primaryClass  = "cs.NE",
  eprint        = "1902.04760"
}

@ARTICLE{Novak2018-qq,
  title         = "Bayesian Deep Convolutional Networks with Many Channels are
                   Gaussian Processes",
  author        = "Novak, Roman and Xiao, Lechao and Lee, Jaehoon and Bahri,
                   Yasaman and Yang, Greg and Hron, Jiri and Abolafia, Daniel A
                   and Pennington, Jeffrey and Sohl-Dickstein, Jascha",
  abstract      = "There is a previously identified equivalence between wide
                   fully connected neural networks (FCNs) and Gaussian
                   processes (GPs). This equivalence enables, for instance,
                   test set predictions that would have resulted from a fully
                   Bayesian, infinitely wide trained FCN to be computed without
                   ever instantiating the FCN, but by instead evaluating the
                   corresponding GP. In this work, we derive an analogous
                   equivalence for multi-layer convolutional neural networks
                   (CNNs) both with and without pooling layers, and achieve
                   state of the art results on CIFAR10 for GPs without
                   trainable kernels. We also introduce a Monte Carlo method to
                   estimate the GP corresponding to a given neural network
                   architecture, even in cases where the analytic form has too
                   many terms to be computationally feasible. Surprisingly, in
                   the absence of pooling layers, the GPs corresponding to CNNs
                   with and without weight sharing are identical. As a
                   consequence, translation equivariance, beneficial in finite
                   channel CNNs trained with stochastic gradient descent (SGD),
                   is guaranteed to play no role in the Bayesian treatment of
                   the infinite channel limit - a qualitative difference
                   between the two regimes that is not present in the FCN case.
                   We confirm experimentally, that while in some scenarios the
                   performance of SGD-trained finite CNNs approaches that of
                   the corresponding GPs as the channel count increases, with
                   careful tuning SGD-trained CNNs can significantly outperform
                   their corresponding GPs, suggesting advantages from SGD
                   training compared to fully Bayesian parameter estimation.",
  month         =  oct,
  year          =  2018,
  archivePrefix = "arXiv",
  primaryClass  = "stat.ML",
  eprint        = "1810.05148"
}

@ARTICLE{Lee2017-sm,
  title         = "Deep Neural Networks as Gaussian Processes",
  author        = "Lee, Jaehoon and Bahri, Yasaman and Novak, Roman and
                   Schoenholz, Samuel S and Pennington, Jeffrey and
                   Sohl-Dickstein, Jascha",
  abstract      = "It has long been known that a single-layer fully-connected
                   neural network with an i.i.d. prior over its parameters is
                   equivalent to a Gaussian process (GP), in the limit of
                   infinite network width. This correspondence enables exact
                   Bayesian inference for infinite width neural networks on
                   regression tasks by means of evaluating the corresponding
                   GP. Recently, kernel functions which mimic multi-layer
                   random neural networks have been developed, but only outside
                   of a Bayesian framework. As such, previous work has not
                   identified that these kernels can be used as covariance
                   functions for GPs and allow fully Bayesian prediction with a
                   deep neural network. In this work, we derive the exact
                   equivalence between infinitely wide deep networks and GPs.
                   We further develop a computationally efficient pipeline to
                   compute the covariance function for these GPs. We then use
                   the resulting GPs to perform Bayesian inference for wide
                   deep neural networks on MNIST and CIFAR-10. We observe that
                   trained neural network accuracy approaches that of the
                   corresponding GP with increasing layer width, and that the
                   GP uncertainty is strongly correlated with trained network
                   prediction error. We further find that test performance
                   increases as finite-width trained networks are made wider
                   and more similar to a GP, and thus that GP predictions
                   typically outperform those of finite-width networks. Finally
                   we connect the performance of these GPs to the recent theory
                   of signal propagation in random neural networks.",
  month         =  nov,
  year          =  2017,
  archivePrefix = "arXiv",
  primaryClass  = "stat.ML",
  eprint        = "1711.00165"
}

@ARTICLE{De_G_Matthews2018-vo,
  title         = "Gaussian Process Behaviour in Wide Deep Neural Networks",
  author        = "de G. Matthews, Alexander G and Rowland, Mark and Hron, Jiri
                   and Turner, Richard E and Ghahramani, Zoubin",
  abstract      = "Whilst deep neural networks have shown great empirical
                   success, there is still much work to be done to understand
                   their theoretical properties. In this paper, we study the
                   relationship between random, wide, fully connected,
                   feedforward networks with more than one hidden layer and
                   Gaussian processes with a recursive kernel definition. We
                   show that, under broad conditions, as we make the
                   architecture increasingly wide, the implied random function
                   converges in distribution to a Gaussian process, formalising
                   and extending existing results by Neal (1996) to deep
                   networks. To evaluate convergence rates empirically, we use
                   maximum mean discrepancy. We then compare finite Bayesian
                   deep networks from the literature to Gaussian processes in
                   terms of the key predictive quantities of interest, finding
                   that in some cases the agreement can be very close. We
                   discuss the desirability of Gaussian process behaviour and
                   review non-Gaussian alternative models from the literature.",
  month         =  apr,
  year          =  2018,
  archivePrefix = "arXiv",
  primaryClass  = "stat.ML",
  eprint        = "1804.11271"
}

@ARTICLE{Garriga-Alonso2018-jx,
  title         = "Deep Convolutional Networks as shallow Gaussian Processes",
  author        = "Garriga-Alonso, Adri{\`a} and Rasmussen, Carl Edward and
                   Aitchison, Laurence",
  abstract      = "We show that the output of a (residual) convolutional neural
                   network (CNN) with an appropriate prior over the weights and
                   biases is a Gaussian process (GP) in the limit of infinitely
                   many convolutional filters, extending similar results for
                   dense networks. For a CNN, the equivalent kernel can be
                   computed exactly and, unlike ``deep kernels'', has very few
                   parameters: only the hyperparameters of the original CNN.
                   Further, we show that this kernel has two properties that
                   allow it to be computed efficiently; the cost of evaluating
                   the kernel for a pair of images is similar to a single
                   forward pass through the original CNN with only one filter
                   per layer. The kernel equivalent to a 32-layer ResNet
                   obtains 0.84\% classification error on MNIST, a new record
                   for GPs with a comparable number of parameters.",
  month         =  aug,
  year          =  2018,
  archivePrefix = "arXiv",
  primaryClass  = "stat.ML",
  eprint        = "1808.05587"
}


@MISC{Wilson_undated-sv,
  title        = "Bayesian neural networks from a Gaussian process perspective",
  author       = "Wilson, Andrew Gordon",
  howpublished = "\url{http://gpss.cc/gpss20/slides/Wilson2020_part2.pdf}",
  note         = "Accessed: 2021-5-26",
  year = {2020}
}

@article{shahriari2015taking,
  title={Taking the human out of the loop: A review of {B}ayesian optimization},
  author={Shahriari, Bobak and Swersky, Kevin and Wang, Ziyu and Adams, Ryan P and De Freitas, Nando},
  journal={Proceedings of the IEEE},
  volume={104},
  number={1},
  pages={148--175},
  year={2015},
  publisher={IEEE}
}


@ARTICLE{Blei2014-gr,
  title     = "Build, Compute, Critique, Repeat: Data Analysis with Latent
               Variable Models",
  author    = "Blei, David M",
  abstract  = "We survey latent variable models for solving data-analysis
               problems. A latent variable model is a probabilistic model that
               encodes hidden patterns in the data. We uncover these patterns
               from their conditional distribution and use them to summarize
               data and form predictions. Latent variable models are important
               in many fields, including computational biology, natural
               language processing, and social network analysis. Our
               perspective is that models are developed iteratively: We build a
               model, use it to analyze data, assess how it succeeds and fails,
               revise it, and repeat. We describe how new research has
               transformed these essential activities. First, we describe
               probabilistic graphical models, a language for formulating
               latent variable models. Second, we describe mean field
               variational inference, a generic algorithm for approximating
               conditional distributions. Third, we describe how to use our
               analyses to solve problems: exploring the data, forming
               predictions, and pointing us in the direction of improved
               models.",
  journal   = "Annu. Rev. Stat. Appl.",
  publisher = "Annual Reviews",
  volume    =  1,
  number    =  1,
  pages     = "203--232",
  month     =  jan,
  year      =  2014
}

@article{diaconis1980finite,
  title={Finite exchangeable sequences},
  author={Diaconis, Persi and Freedman, David},
  journal={The Annals of Probability},
  pages={745--764},
  year={1980},
  publisher={JSTOR}
}

@article{diaconis1980finetti,
  title={de {F}inetti's theorem for {M}arkov chains},
  author={Diaconis, Persi and Freedman, David},
  journal={The Annals of Probability},
  pages={115--130},
  year={1980},
  publisher={JSTOR}
}

@article{aldous1981representations,
  title={Representations for partially exchangeable arrays of random variables},
  author={Aldous, David J},
  journal={Journal of Multivariate Analysis},
  volume={11},
  number={4},
  pages={581--598},
  year={1981},
  publisher={Elsevier}
}

@techreport{hoover1979relations,
title={Relations on Probability Spaces and Arrays of Random Variables.},
author={Hoover, Douglas},
institution={Institute for Advanced Study, Princeton, NJ},
year={1979}
}

@article{geyer2011introduction,
  title={Introduction to {M}arkov chain {M}onte {C}arlo},
  author={Geyer, Charles J},
  journal={Handbook of Markov chain Monte Carlo},
  volume={20116022},
  pages={45},
  year={2011},
  publisher={Boca Raton}
}

@book{levin2017markov,
  title={Markov chains and mixing times},
  author={Levin, David A and Peres, Yuval},
  year={2017},
  publisher={American Mathematical Soc.}
}

@book{meyn2012markov,
  title={Markov chains and stochastic stability},
  author={Meyn, Sean P and Tweedie, Richard L},
  year={2012},
  publisher={Springer Science \& Business Media}
}

@article{bach2005probabilistic,
  title={A probabilistic interpretation of canonical correlation analysis},
  author={Bach, Francis R and Jordan, Michael I},
  year={2005},
  publisher={Technical Report 688, Department of Statistics, University of California~…}
}

@article{witten2009penalized,
  title={A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis},
  author={Witten, Daniela M and Tibshirani, Robert and Hastie, Trevor},
  journal={Biostatistics},
  volume={10},
  number={3},
  pages={515--534},
  year={2009},
  publisher={Oxford University Press}
}

@article{wainwright2008graphical,
  title={Graphical models, exponential families, and variational inference},
  author={Wainwright, Martin J and Jordan, Michael I and others},
  journal={Foundations and Trends{\textregistered} in Machine Learning},
  volume={1},
  number={1--2},
  pages={1--305},
  year={2008},
  publisher={Now Publishers, Inc.}
}

@article{duchi2018introductory,
  title={Introductory lectures on stochastic optimization},
  author={Duchi, John C},
  journal={The mathematics of data},
  volume={25},
  pages={99--186},
  year={2018}
}

@article{bottou1998online,
  title={Online learning and stochastic approximations},
  author={Bottou, L{\'e}on and others},
  journal={On-line learning in neural networks},
  volume={17},
  number={9},
  pages={142},
  year={1998}
}

@incollection{robbins1971convergence,
  title={A convergence theorem for non negative almost supermartingales and some applications},
  author={Robbins, Herbert and Siegmund, David},
  booktitle={Optimizing methods in statistics},
  pages={233--257},
  year={1971},
  publisher={Elsevier}
}

@article{duchi2011adaptive,
  title={Adaptive subgradient methods for online learning and stochastic optimization.},
  author={Duchi, John and Hazan, Elad and Singer, Yoram},
  journal={Journal of machine learning research},
  volume={12},
  number={7},
  year={2011}
}

@article{kingma2014adam,
  title={Adam: A method for stochastic optimization},
  author={Kingma, Diederik P and Ba, Jimmy},
  journal={arXiv preprint arXiv:1412.6980},
  year={2014}
}

@article{vincent2010stacked,
  title={Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion.},
  author={Vincent, Pascal and Larochelle, Hugo and Lajoie, Isabelle and Bengio, Yoshua and Manzagol, Pierre-Antoine and Bottou, L{\'e}on},
  journal={Journal of machine learning research},
  volume={11},
  number={12},
  year={2010}
}

@phdthesis{lecun1987modeles,
  title={Modeles connexionnistes de lapprentissage},
  author={LeCun, Yann},
  year={1987},
  school={These de Doctorat, Universite Paris}
}

@article{hinton1993autoencoders,
  title={Autoencoders, minimum description length and Helmholtz free energy},
  author={Hinton, Geoffrey E and Zemel, Richard},
  journal={Advances in neural information processing systems},
  volume={6},
  year={1993}
}

@article{bourlard1988auto,
  title={Auto-association by multilayer perceptrons and singular value decomposition},
  author={Bourlard, Herv{\'e} and Kamp, Yves},
  journal={Biological cybernetics},
  volume={59},
  number={4},
  pages={291--294},
  year={1988},
  publisher={Springer}
}


@ARTICLE{Hinton2006-ga,
  title    = "Reducing the dimensionality of data with neural networks",
  author   = "Hinton, G E and Salakhutdinov, R R",
  abstract = "High-dimensional data can be converted to low-dimensional codes
              by training a multilayer neural network with a small central
              layer to reconstruct high-dimensional input vectors. Gradient
              descent can be used for fine-tuning the weights in such
              ``autoencoder'' networks, but this works well only if the initial
              weights are close to a good solution. We describe an effective
              way of initializing the weights that allows deep autoencoder
              networks to learn low-dimensional codes that work much better
              than principal components analysis as a tool to reduce the
              dimensionality of data.",
  journal  = "Science",
  volume   =  313,
  number   =  5786,
  pages    = "504--507",
  month    =  jul,
  year     =  2006,
  language = "en"
}

@book{Goodfellow-et-al-2016,
    title={Deep Learning},
    author={Ian Goodfellow and Yoshua Bengio and Aaron Courville},
    publisher={MIT Press},
    note={\url{http://www.deeplearningbook.org}},
    year={2016}
}


@ARTICLE{Kingma2014-xn,
  title     = "Auto-encoding variational {B}ayes",
  author    = "Kingma, D P and Welling, M",
  journal   = "arXiv preprint arXiv:1312.6114",
  publisher = "arxiv.org",
  year      =  2014
}


@ARTICLE{Rezende2014-ym,
  title         = "Stochastic Backpropagation and Approximate Inference in Deep
                   Generative Models",
  author        = "Rezende, Danilo Jimenez and Mohamed, Shakir and Wierstra,
                   Daan",
  month         =  jan,
  year          =  2014,
  archivePrefix = "arXiv",
  primaryClass  = "stat.ML",
  eprint        = "1401.4082"
}

@article{williams1992simple,
  title={Simple statistical gradient-following algorithms for connectionist reinforcement learning},
  author={Williams, Ronald J},
  journal={Machine learning},
  volume={8},
  number={3},
  pages={229--256},
  year={1992},
  publisher={Springer}
}

@article{mohamed2020monte,
  title={Monte {C}arlo Gradient Estimation in Machine Learning.},
  author={Mohamed, Shakir and Rosca, Mihaela and Figurnov, Michael and Mnih, Andriy},
  journal={Journal of Machine Learning Research},
  volume={21},
  number={132},
  pages={1--62},
  year={2020}
}

@article{rabiner1986introduction,
  title={An introduction to hidden {M}arkov models},
  author={Rabiner, Lawrence and Juang, Biinghwang},
  journal={ieee assp magazine},
  volume={3},
  number={1},
  pages={4--16},
  year={1986},
  publisher={IEEE}
}

@article{girolami2006variational,
  title={Variational {B}ayesian multinomial probit regression with {G}aussian process priors},
  author={Girolami, Mark and Rogers, Simon},
  journal={Neural Computation},
  volume={18},
  number={8},
  pages={1790--1817},
  year={2006},
  publisher={MIT Press}
}

@article{albert1993bayesian,
  title={Bayesian analysis of binary and polychotomous response data},
  author={Albert, James H and Chib, Siddhartha},
  journal={Journal of the American statistical Association},
  volume={88},
  number={422},
  pages={669--679},
  year={1993},
  publisher={Taylor \& Francis}
}

@article{brown2002time,
  title={The time-rescaling theorem and its application to neural spike train data analysis},
  author={Brown, Emery N and Barbieri, Riccardo and Ventura, Val{\'e}rie and Kass, Robert E and Frank, Loren M},
  journal={Neural computation},
  volume={14},
  number={2},
  pages={325--346},
  year={2002},
  publisher={MIT Press One Rogers Street, Cambridge, MA 02142-1209, USA journals-info~…}
}

@article{hawkes1971spectra,
  title={Spectra of some self-exciting and mutually exciting point processes},
  author={Hawkes, Alan G},
  journal={Biometrika},
  volume={58},
  number={1},
  pages={83--90},
  year={1971},
  publisher={Oxford University Press}
}

@inproceedings{linderman2014discovering,
  title={Discovering latent network structure in point process data},
  author={Linderman, Scott and Adams, Ryan},
  booktitle={International Conference on Machine Learning},
  pages={1413--1421},
  year={2014},
  organization={PMLR}
}

@inproceedings{adams2009tractable,
  title={Tractable nonparametric {B}ayesian inference in Poisson processes with {G}aussian process intensities},
  author={Adams, Ryan Prescott and Murray, Iain and MacKay, David JC},
  booktitle={Proceedings of the 26th Annual International Conference on Machine Learning},
  pages={9--16},
  year={2009}
}

@article{wang2022spatiotemporal,
  title={Spatiotemporal Clustering with {N}eyman-{S}cott Processes via Connections to {B}ayesian Nonparametric Mixture Models},
  author={Wang, Yixin and Degleris, Anthony and Williams, Alex H and Linderman, Scott W},
  journal={arXiv preprint arXiv:2201.05044},
  year={2022}
}

@article{miller2018mixture,
  title={Mixture models with a prior on the number of components},
  author={Miller, Jeffrey W and Harrison, Matthew T},
  journal={Journal of the American Statistical Association},
  volume={113},
  number={521},
  pages={340--356},
  year={2018},
  publisher={Taylor \& Francis}
}

@article{bhattacharya2011sparse,
  title={Sparse {B}ayesian infinite factor models},
  author={Bhattacharya, Anirban and Dunson, David B},
  journal={Biometrika},
  pages={291--306},
  year={2011}
}

@article{lotfi2022bayesian,
  title={Bayesian Model Selection, the Marginal Likelihood, and Generalization},
  author={Lotfi, Sanae and Izmailov, Pavel and Benton, Gregory and Goldblum, Micah and Wilson, Andrew Gordon},
  journal={arXiv preprint arXiv:2202.11678},
  year={2022}
}

@article{neal2001annealed,
  title={Annealed importance sampling},
  author={Neal, Radford M},
  journal={Statistics and computing},
  volume={11},
  number={2},
  pages={125--139},
  year={2001},
  publisher={Springer}
}

@article{eddy2004hidden,
  title={What is a hidden {M}arkov model?},
  author={Eddy, Sean R},
  journal={Nature biotechnology},
  volume={22},
  number={10},
  pages={1315--1316},
  year={2004},
  publisher={Nature Publishing Group UK London}
}

@article{wiltschko2015mapping,
  title={Mapping sub-second structure in mouse behavior},
  author={Wiltschko, Alexander B and Johnson, Matthew J and Iurilli, Giuliano and Peterson, Ralph E and Katon, Jesse M and Pashkovski, Stan L and Abraira, Victoria E and Adams, Ryan P and Datta, Sandeep Robert},
  journal={Neuron},
  volume={88},
  number={6},
  pages={1121--1135},
  year={2015},
  publisher={Elsevier}
}
@article{kalman1960new,
  author={Kalman, Rudolf Emil},
  title={A new approach to linear filtering and prediction problems},
  journal={Journal of Basic Engineering},
  volume={82},
  number={1},
  pages={35--45},
  year={1960}
}

@article{rauch1965maximum,
  author={Rauch, Herbert E and Striebel, Charlotte T and Tung, F},
  title={Maximum likelihood estimates of linear dynamic systems},
  journal={AIAA Journal},
  volume={3},
  number={8},
  pages={1445--1450},
  year={1965}
}

@book{shumway2000time,
  author={Shumway, Robert H and Stoffer, David S},
  title={Time Series Analysis and Its Applications},
  publisher={Springer},
  year={2000}
}

@book{sutton2018reinforcement,
  title={Reinforcement Learning: An Introduction},
  author={Sutton, Richard S and Barto, Andrew G},
  edition={2nd},
  year={2018},
  publisher={MIT Press}
}

@article{williams1992simple,
  title={Simple statistical gradient-following algorithms for connectionist reinforcement learning},
  author={Williams, Ronald J},
  journal={Machine Learning},
  volume={8},
  number={3},
  pages={229--256},
  year={1992},
  publisher={Springer}
}

@article{schulman2017proximal,
  title={Proximal policy optimization algorithms},
  author={Schulman, John and Wolski, Filip and Dhariwal, Prafulla and Radford, Alec and Klimov, Oleg},
  journal={arXiv preprint arXiv:1707.06347},
  year={2017}
}

@inproceedings{christiano2017deep,
  title={Deep reinforcement learning from human preferences},
  author={Christiano, Paul F and Leike, Jan and Brown, Tom and Martic, Miljan and Legg, Shane and Amodei, Dario},
  booktitle={Advances in Neural Information Processing Systems},
  volume={30},
  year={2017}
}

@article{ouyang2022training,
  title={Training language models to follow instructions with human feedback},
  author={Ouyang, Long and Wu, Jeffrey and Jiang, Xu and Almeida, Diogo and Wainwright, Carroll and Mishkin, Pamela and Zhang, Chong and Agarwal, Sandhini and Slama, Katarina and Ray, Alex and others},
  journal={Advances in Neural Information Processing Systems},
  volume={35},
  pages={27730--27744},
  year={2022}
}

@article{rafailov2024direct,
  title={Direct preference optimization: Your language model is secretly a reward model},
  author={Rafailov, Rafael and Sharma, Archit and Mitchell, Eric and Manning, Christopher D and Ermon, Stefano and Finn, Chelsea},
  journal={Advances in Neural Information Processing Systems},
  volume={36},
  year={2024}
}

@article{ziegler2019fine,
  title={Fine-tuning language models from human preferences},
  author={Ziegler, Daniel M and Stiennon, Nisan and Wu, Jeffrey and Brown, Tom B and Radford, Alec and Amodei, Dario and Christiano, Paul and Irving, Geoffrey},
  journal={arXiv preprint arXiv:1909.08593},
  year={2019}
}

@inproceedings{katharopoulos2020transformers,
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