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.
New algorithms improve convergence rates for non-log-concave sampling and log-partition estimation.
Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition function, based on convex combinations of distributions in the exponential domain, th…
Paper proposes a new method to learn EBMs and their partition function.
Recent research has made significant progress on the problem of bounding log partition functions for exponential family graphical models. Such bounds have associated dual parameters that are often used as heuristic estimates of the marginal probabilities required in inference and learning. However these variational est…
We consider log-supermodular models on binary variables, which are probabilistic models with negative log-densities which are submodular. These models provide probabilistic interpretations of common combinatorial optimization tasks such as image segmentation. In this paper, we focus primarily on parameter estimation in…
We propose a relaxation-based approximate inference algorithm that samples near-MAP configurations of a binary pairwise Markov random field. We experiment on MAP inference tasks in several restricted Boltzmann machines. We also use our underlying sampler to estimate the log-partition function of restricted Boltzmann ma…
Paper optimizes change detection in unnormalized distributions.
We study approximations of the partition function of dense graphical models. Partition functions of graphical models play a fundamental role is statistical physics, in statistics and in machine learning. Two of the main methods for approximating the partition function are Markov Chain Monte Carlo and Variational Method…
We develop a variant of multiclass logistic regression that is significantly more robust to noise. The algorithm has one weight vector per class and the surrogate loss is a function of the linear activations (one per class). The surrogate loss of an example with linear activation vector and class has t…
We introduce a new class of lower bounds on the log partition function of a Markov random field which makes use of a reversed Jensen's inequality. In particular, our method approximates the intractable distribution using a linear combination of spanning trees with negative weights. This technique is a lower-bound count…
Many problems in machine learning are naturally expressed in the language of undirected graphical models. Here, we propose black-box learning and inference algorithms for undirected models that optimize a variational approximation to the log-likelihood of the model. Central to our approach is an upper bound on the log-…
Paper improves variational inference on Boolean hypercube using quantum methods.
For many large undirected models that arise in real-world applications, exact maximumlikelihood training is intractable, because it requires computing marginal distributions of the model. Conditional training is even more difficult, because the partition function depends not only on the parameters, but also on the obse…
We analyze a reweighted version of the Kikuchi approximation for estimating the log partition function of a product distribution defined over a region graph. We establish sufficient conditions for the concavity of our reweighted objective function in terms of weight assignments in the Kikuchi expansion, and show that a…
This paper introduces the Metric-Free Natural Gradient (MFNG) algorithm for training Boltzmann Machines. Similar in spirit to the Hessian-Free method of Martens [8], our algorithm belongs to the family of truncated Newton methods and exploits an efficient matrix-vector product to avoid explicitely storing the natural g…
We propose a black-box algorithm called {\it Adversarial Variational Inference and Learning} (AdVIL) to perform inference and learning on a general Markov random field (MRF). AdVIL employs two variational distributions to approximately infer the latent variables and estimate the partition function of an MRF, respective…
Entropy analysis via kernel methods for probabilistic inference.
The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each time solving for the most likely configuration. We derive an entire family of r…
It is known that fixed points of loopy belief propagation (BP) correspond to stationary points of the Bethe variational problem, where we minimize the Bethe free energy subject to normalization and marginalization constraints. Unfortunately, this does not entirely explain BP because BP is a dual rather than primal algo…
Geometric analysis improves convergence of variational inference.
We give polynomial-time algorithms for the exact computation of lowest-energy (ground) states, worst margin violators, log partition functions, and marginal edge probabilities in certain binary undirected graphical models. Our approach provides an interesting alternative to the well-known graph cut paradigm in that it …
The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's razor" interpretation. Unfortunately, calculating the potentials in the maximum-entro…
The paper solves portfolio selection using Rényi divergence and optimization.
Submodular extensions of an energy function can be used to efficiently compute approximate marginals via variational inference. The accuracy of the marginals depends crucially on the quality of the submodular extension. To identify the best possible extension, we show an equivalence between the submodular extensions of…
Looking for associations among multiple variables is a topical issue in statistics due to the increasing amount of data encountered in biology, medicine and many other domains involving statistical applications. Graphical models have recently gained popularity for this purpose in the statistical literature. Following t…
Scaling multinomial logistic regression to datasets with very large number of data points and classes is challenging. This is primarily because one needs to compute the log-partition function on every data point. This makes distributing the computation hard. In this paper, we present a distributed stochastic gradient d…
Extends likelihood ratio exponential families to analyze various optimization methods.
Paper analyzes latent space geometry in generative models using Fisher information.
We present a novel k-way high-dimensional graphical model called the Generalized Root Model (GRM) that explicitly models dependencies between variable sets of size k > 2---where k = 2 is the standard pairwise graphical model. This model is based on taking the k-th root of the original sufficient statistics of any univa…
We use SMC with twist functions to improve probabilistic inference in LLMs.
We consider parametric exponential families of dimension on the real line. We study a variant of \textit{boundary crossing probabilities} coming from the multi-armed bandit literature, in the case when the real-valued distributions form an exponential family of dimension . Formally, our result is a concentration…
Paper addresses inefficiency in converting EFGs to NFGs for learning.
New MI bounds improve estimation in deep generative models.
In this paper, we consider an infinite dimensional exponential family, of probability densities, which are parametrized by functions in a reproducing kernel Hilbert space, and show it to be quite rich in the sense that a broad class of densities on can be approximated arbitrarily well i…