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.
Optimal SQ bounds for learning binary product distributions and Ising models.
We describe discrete restricted Boltzmann machines: probabilistic graphical models with bipartite interactions between visible and hidden discrete variables. Examples are binary restricted Boltzmann machines and discrete naive Bayes models. We detail the inference functions and distributed representations arising in th…
We study the problem of learning a distribution from samples, when the underlying distribution is a mixture of product distributions over discrete domains. This problem is motivated by several practical applications such as crowd-sourcing, recommendation systems, and learning Boolean functions. The existing solutions e…
New model optimizes oil product distribution via pipelines.
We derive relations between theoretical properties of restricted Boltzmann machines (RBMs), popular machine learning models which form the building blocks of deep learning models, and several natural notions from discrete mathematics and convex geometry. We give implications and equivalences relating RBM-representable …
Improved sample and time complexity for identifying mixtures of product distributions.
Discrete exterior calculus shows natural properties of wedge product and averaging.
A new gradient estimator for categorical distributions reduces bias and variance.
Efficiently estimate Boolean product distribution parameters from truncated samples.
Sum-Product Networks (SPNs) can be regarded as a form of deep graphical models that compactly represent deeply factored and mixed distributions. An SPN is a rooted directed acyclic graph (DAG) consisting of a set of leaves (corresponding to base distributions), a set of sum nodes (which represent mixtures of their chil…
Example found of subgroup not a lattice in product of Lie groups
We consider the problem of inference in discrete probabilistic models, that is, distributions over subsets of a finite ground set. These encompass a range of well-known models in machine learning, such as determinantal point processes and Ising models. Locally-moving Markov chain Monte Carlo algorithms, such as the Gib…
Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to …
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a continuous master equation. The derivation of elementary rates from known stationa…
A new method for generative modeling of discrete data using geometric latent subspaces.
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equatio…
GBS uses machine learning to design products based on consumer preferences.
Proves finite measure implies product structure for certain discrete subgroups.
The paper analyzes the probabilistic structure of DDPMs and bounds their sampling error.
Study of discrete analogues of Atiyah sequence in principal bundles.
Paper improves likelihood estimation for discrete distributions.
Researchers create spectral triples for twisted crossed products using Kasparov's external product.
Feature selection can facilitate the learning of mixtures of discrete random variables as they arise, e.g. in crowdsourcing tasks. Intuitively, not all workers are equally reliable but, if the less reliable ones could be eliminated, then learning should be more robust. By analogy with Gaussian mixture models, we seek a…
Combination theorems for convex projective geometry subgroups.
Paper proposes a method to estimate consumer valuations from bundle sales data.
Bayesian reinforcement learning (BRL) encodes prior knowledge of the world in a model and represents uncertainty in model parameters by maintaining a probability distribution over them. This paper presents Monte Carlo BRL (MC-BRL), a simple and general approach to BRL. MC-BRL samples a priori a finite set of hypotheses…
Branching Flows generates sequences of varying lengths using binary trees.
Graphically discrete groups have strong rigidity properties.
We propose simple conditions equivalent to the discreteness of the spectrum of the Laplace-Beltrami operator on a class of Riemannian manifolds close to warped products. For this class of manifolds we establish a relationship between discreteness of the spectrum and stochastic incompleteness.
Novel approach for estimating joint probability densities using tensor decompositions and dictionaries.
The abstract discusses compact quotients of Riemannian products by discrete subgroups, generalizing Inoue-Bombieri surfaces.
We introduce Network Maximal Correlation (NMC) as a multivariate measure of nonlinear association among random variables. NMC is defined via an optimization that infers transformations of variables by maximizing aggregate inner products between transformed variables. For finite discrete and jointly Gaussian random vari…
We prove the formula for the topological complexity of the free product of discrete groups with cohomological dimension >2.
New algorithms test independence with fewer samples by using predictive information.
Paper proposes a new generative model for discrete distributions using flows on submanifolds.
The paper extends statistical estimation techniques under differential privacy.
Study higher rank inner products and their tilings to describe tori degenerations.
Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lower-dimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such models can be very computationally expensive when there are many datapoints and …
Discrete Green's functions are the inverses or pseudo-inverses of combinatorial Laplacians. We present compact formulas for discrete Green's functions, in terms of the eigensystems of corresponding Laplacians, for products of regular graphs with or without boundary. Explicit formulas are derived for the cycle, torus, a…
New method compresses non-Gaussian distributions exponentially.
New matrix ensembles better match deep neural network spectral densities.
This paper analyzes the bias of inexact MCMC methods in high dimensions.
The paper analyzes rates of convergence for optimal transport map estimators using barycentric projections.
Paper develops a gradient-like proposal for discrete distributions without requiring natural differentiability.
New method for pricing financial products without no-arbitrage condition.
We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated with a dimension partition tree. The distribution is assumed to admit a density …
In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas…
We study differential operators, whose coefficients define noncommutative algebras. As algebra of coefficients, we consider crossed products, corresponding to action of a discrete group on a smooth manifold. We give index formulas for Euler, signature and Dirac operators twisted by projections over the crossed product.…