arXiv research

The paper analyzes the randomized midpoint method for Langevin diffusions, revealing biases and asymptotic properties.

Study optimal hedging for claims with random weights in discrete time.

Random Gaussian noise and pixel discretization improve image classifier robustness.

The reparameterization trick enables optimizing large scale stochastic computation graphs via gradient descent. The essence of the trick is to refactor each stochastic node into a differentiable function of its parameters and a random variable with fixed distribution. After refactoring, the gradients of the loss propag…

We explore a new method for discrete-time control problems using randomization and entropy.

We present extremal constructions connected with the property of simplicial collapsibility. (1) For each $d \ge 2$, there are collapsible (and shellable) simplicial $d$-complexes with only one free face. Also, there are non-evasive $d$-complexes with only two free faces. (Both results are optimal in all dimensions.) (2…

In this paper, we face the problem of simulating discrete random variables with general and varying distributions in a scalable framework, where fully parallelizable operations should be preferred. The new paradigm is inspired by the context of discrete choice models. Compared to classical algorithms, we add paralleliz…

1) We introduce random discrete Morse theory as a computational scheme to measure the complicatedness of a triangulation. The idea is to try to quantify the frequence of discrete Morse matchings with a certain number of critical cells. Our measure will depend on the topology of the space, but also on how nicely the spa…

New estimator reduces variance in discrete random variables.

Discretizes diffusion processes on covering spaces.

Simplified analysis of diffusion models using discrete random variables.

Paper proposes a new estimator for generic discrete distributions.

The paper confirms a conjecture about optimal expected utility in discrete-time markets approaching a continuous-time model.

Generative model for joint discrete distributions using randomized assignment flows.

Neural networks approximate random utility models for choice prediction.

Algorithm reduces support of discrete measures by integrating against functions.

Efficient method certifies robustness of discrete data models, especially graphs.

Optimal transport is #P-hard when components are independent, even with approximate solutions.

IDF++ improves integer discrete flows for lossless compression.

We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a lower-dimensional Euclidean space using random projections. Subsequently, estimation …

Study diffusions and random walks on hyperbolic spaces, focusing on their Martin boundaries.

New algorithm learns halfspaces over hypercube with random bit flips.

We present an intriguing discovery related to Random Fourier Features: in Gaussian kernel approximation, replacing the random Gaussian matrix by a properly scaled random orthogonal matrix significantly decreases kernel approximation error. We call this technique Orthogonal Random Features (ORF), and provide theoretical…

Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a diffusion equation with a diffusion coefficient that inversely depends on the dat…

In earlier work we introduced geometrically natural probability measures on the group of all Möbius transformations in order to study "random" groups of Möbius transformations, random surfaces, and in particular random two-generator groups, that is groups where the generators are selected randomly, with a view to estim…

The paper proves that certain spaces have injective balls of any radius.

Normalizing flows are a powerful class of generative models for continuous random variables, showing both strong model flexibility and the potential for non-autoregressive generation. These benefits are also desired when modeling discrete random variables such as text, but directly applying normalizing flows to discret…

New methods for calculating curvature in graph theory.

Direct policy gradients optimize policies in discrete action spaces using sampling.

In a way similar to the continuous case formally, we define in different but equivalent manners the difference discrete connection and curvature on discrete vector bundle over the regular lattice as base space. We deal with the difference operators as the discrete counterparts of the derivatives based upon the differen…

Random Gaussian fields on 4D Riemannian manifolds with conformal invariance.

Paper improves neural network robustness certification with tighter radii estimates.

Continuized Nesterov acceleration accelerates stochastic gradient descent and gossip algorithms.

New wavelets use Monte Carlo for efficient discretization.

Study provides convergence guarantees for discrete diffusion models on finite and infinite state spaces.

Efficient algorithm approximates discrete random variables with minimal Kolmogorov distance.

Functional adapts to graph structures for machine learning applications.

Discrete time random walks on a finite set naturally translate via a one-to-one correspondence to discrete Laplace operators. Typically, Ollivier curvature has been investigated via random walks. We first extend the definition of Ollivier curvature to general weighted graphs and then give a strikingly simple representa…

Graphs approximate semigroups for diffusion on Riemannian manifolds.

Gradient estimation techniques applied to programs with randomness in high energy physics.

The paper confirms a conjecture about optimal expected utility in markets with insider information.

New algorithm approximates maximum of certain distributions on subsets.

A new method for efficient inference in probabilistic programs with mixed support.

The paper develops methods to estimate frequencies in large discrete data sets with improved coverage and robustness.

Universal inequalities for Laplacian eigenvalues on discrete groups.

Bayesian optimization adapted for discrete spaces using random mappings.

GCNs converge and remain stable on large random graphs, revealing geometric insights.

Study shows how discrete graph curvature relates to manifold curvature.