A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
EFDA extends LDA to non-Gaussian models using exponential families.
Kernel discriminant analysis uses nonlinear embeddings to improve classification.
Study shows MDA's effectiveness even when more components are assumed than in actual data.
Exponential family extensions of principal component analysis (EPCA) have received a considerable amount of attention in recent years, demonstrating the growing need for basic modeling tools that do not assume the squared loss or Gaussian distribution. We extend the EPCA model toolbox by presenting the first exponentia…
This work presents an analysis of the discriminators used in Generative Adversarial Networks (GANs) for Video. We show that unconstrained video discriminator architectures induce a loss surface with high curvature which make optimisation difficult. We also show that this curvature becomes more extreme as the maximal ke…
New Thompson sampling algorithm reduces regret for exponential family bandits.
Thompson Sampling has been demonstrated in many complex bandit models, however the theoretical guarantees available for the parametric multi-armed bandit are still limited to the Bernoulli case. Here we extend them by proving asymptotic optimality of the algorithm using the Jeffreys prior for 1-dimensional exponential …
Incorporating feature selection into a classification or regression method often carries a number of advantages. In this paper we formalize feature selection specifically from a discriminative perspective of improving classification/regression accuracy. The feature selection method is developed as an extension to the r…
New method for robust PCA with exponential family distributions.
Improves variational inference for sparse models using mixtures of exponential families.
New bounds for score matching in polynomial exponential families.
A theoretical framework for non-negative matrix factorization based on generalized dual Kullback-Leibler divergence, which includes members of the exponential family of models, is proposed. A family of algorithms is developed using this framework and its convergence proven using the Expectation-Maximization algorithm. …
Paper explores duality in DPPs using embedding structure analysis.
This paper analyzes VAE approximation errors in conditional exponential families.
We consider the design of prediction market mechanisms known as automated market makers. We show that we can design these mechanisms via the mold of \emph{exponential family distributions}, a popular and well-studied probability distribution template used in statistics. We give a full development of this relationship a…
New DP framework using data truncation for efficient estimation.
There has been an explosion of interest in statistical models for analyzing network data, and considerable interest in the class of exponential random graph (ERG) models, especially in connection with difficulties in computing maximum likelihood estimates. The issues associated with these difficulties relate to the bro…
While Generative Adversarial Networks (GANs) have empirically produced impressive results on learning complex real-world distributions, recent works have shown that they suffer from lack of diversity or mode collapse. The theoretical work of Arora et al. suggests a dilemma about GANs' statistical properties: powerful d…
We present a new method which generalizes subspace learning based on eigenvalue and generalized eigenvalue problems. This method, Roweis Discriminant Analysis (RDA), is named after Sam Roweis to whom the field of subspace learning owes significantly. RDA is a family of infinite number of algorithms where Principal Comp…
Paper introduces kernel deformed exponential families for sparse continuous attention.
The study of private inference has been sparked by growing concern regarding the analysis of data when it stems from sensitive sources. We present the first method for private Bayesian inference in exponential families that properly accounts for noise introduced by the privacy mechanism. It is efficient because it work…
New algorithm for efficiently identifying the best arm in stochastic bandits.
Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly…
We study Bayesian discriminative inference given a model family $p(c,\x, θ)$ that is assumed to contain all our prior information but still known to be incorrect. This falls in between "standard" Bayesian generative modeling and Bayesian regression, where the margin $p(\x,θ)$ is known to be uninformative about $p(c|\x,…
Quadratic discriminant analysis (QDA) is a standard tool for classification due to its simplicity and flexibility. Because the number of its parameters scales quadratically with the number of the variables, QDA is not practical, however, when the dimensionality is relatively large. To address this, we propose a novel p…
New method for tensor completion using nonconvex dual total variation.
We show how to estimate a model's test error from unlabeled data, on distributions very different from the training distribution, while assuming only that certain conditional independencies are preserved between train and test. We do not need to assume that the optimal predictor is the same between train and test, or t…
EM algorithm converges in KL divergence for exponential families via mirror descent.
Exponential family distributions are highly useful in machine learning since their calculation can be performed efficiently through natural parameters. The exponential family has recently been extended to the t-exponential family, which contains Student-t distributions as family members and thus allows us to handle noi…
The methods of statistical physics are widely used for modelling complex networks. Building on the recently proposed Equilibrium Expectation approach, we derive a simple and efficient algorithm for maximum likelihood estimation (MLE) of parameters of exponential family distributions - a family of statistical models, th…
New framework assesses neural sensitivity to small perturbations.
The study explores generalized divergences and exponential families with a focus on sufficient conditions and laws of large numbers.
Generative Adversarial Networks (GANs) are a class of generative algorithms that have been shown to produce state-of-the art samples, especially in the domain of image creation. The fundamental principle of GANs is to approximate the unknown distribution of a given data set by optimizing an objective function through a…
New models for analyzing microbiome data with interactions.
Correspondence found between exponential families and affine Grassmannians.
Geometric analysis improves convergence of variational inference.
Nowozin \textit{et al} showed last year how to extend the GAN \textit{principle} to all -divergences. The approach is elegant but falls short of a full description of the supervised game, and says little about the key player, the generator: for example, what does the generator actually converge to if solving the GAN…
We develop a general method for estimating a finite mixture of non-normalized models. Here, a non-normalized model is defined to be a parametric distribution with an intractable normalization constant. Existing methods for estimating non-normalized models without computing the normalization constant are not applicable …
Study the geometry of hydrodynamics equations using diffeomorphism groups.
We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, including Bayesian networks …
Constructing exponential families from statistical manifolds.
Word embeddings are a powerful approach for capturing semantic similarity among terms in a vocabulary. In this paper, we develop exponential family embeddings, a class of methods that extends the idea of word embeddings to other types of high-dimensional data. As examples, we studied neural data with real-valued observ…
Moment polytope of toric exponential families is a projection of a simplex.
Paper proposes Roweisposes for 3D action recognition using generalized eigenvalue problem.
We study online learning under logarithmic loss with regular parametric models. Hedayati and Bartlett (2012b) showed that a Bayesian prediction strategy with Jeffreys prior and sequential normalized maximum likelihood (SNML) coincide and are optimal if and only if the latter is exchangeable, and if and only if the opti…
We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate probability mass in the neighborhood of the observed points, resulting in a non-para…
The versatility of exponential families, along with their attendant convexity properties, make them a popular and effective statistical model. A central issue is learning these models in high-dimensions, such as when there is some sparsity pattern of the optimal parameter. This work characterizes a certain strong conve…
New insights into natural exponential families improve regret bounds for bandit problems.