arXiv research

Shallow neural nets classify objects perfectly if their distribution is linearly separable.

Categorical d-separation criterion simplifies probability graph analysis.

The paper extends optimal transport for linear separability of sheared distributions in supervised learning.

The paper solves optimal bounds for separating data points in high dimensions.

Kernel embeddings separate distinct probability distributions, simplifying testing.

Develops a new framework for causal models on cyclic graphs, solving unique solvability issues.

We propose a new blind source separation algorithm based on mixtures of alpha-stable distributions. Complex symmetric alpha-stable distributions have been recently showed to better model audio signals in the time-frequency domain than classical Gaussian distributions thanks to their larger dynamic range. However, infer…

Separable losses are inconsistent for structured prediction models.

Generative source separation methods such as non-negative matrix factorization (NMF) or auto-encoders, rely on the assumption of an output probability density. Generative Adversarial Networks (GANs) can learn data distributions without needing a parametric assumption on the output density. We show on a speech source se…

New conditions ensure MMDs separate and converge to target distributions.

Sharp bounds for high-probability estimation of discrete distributions.

Refined analysis of Mitra's algorithm for discrete mixtures.

New approach for classification using trigonometric polynomial kernels from signal processing.

New framework for cyclic quantum causal models with graph separation property.

New findings show fixed-kernel discriminators are weaker than feature-learning ones.

In this paper, we presented a novel semi-supervised one-class classification algorithm which assumes that class is linearly separable from other elements. We proved theoretically that class is linearly separable if and only if it is maximal by probability within the sets with the same mean. Furthermore, we presented an…

Sharp bounds for max-sliced Wasserstein distances derived for empirical distributions.

Enhanced FastMNMF for better speech separation.

DG separates successes and failures by gating updates with advantage and surprisal.

Graph convolution improves linear separability and generalizes to out-of-distribution data.

The study shows subgroup separability conditions for specific groups.

For a certain class of distributions, we prove that the linear programming relaxation of $k$-medoids clustering---a variant of $k$-means clustering where means are replaced by exemplars from within the dataset---distinguishes points drawn from nonoverlapping balls with high probability once the number of points drawn a…

The hypothesis that high dimensional data tend to lie in the vicinity of a low dimensional manifold is the basis of manifold learning. The goal of this paper is to develop an algorithm (with accompanying complexity guarantees) for fitting a manifold to an unknown probability distribution supported in a separable Hilber…

We introduce a new approach for designing computationally efficient learning algorithms that are tolerant to noise, and demonstrate its effectiveness by designing algorithms with improved noise tolerance guarantees for learning linear separators. We consider both the malicious noise model and the adversarial label nois…

This paper studies Fenchel-Young losses, a generic way to construct convex loss functions from a regularization function. We analyze their properties in depth, showing that they unify many well-known loss functions and allow to create useful new ones easily. Fenchel-Young losses constructed from a generalized entropy, …

Estimates copula density for complex data distributions.

A Fourier-based learning algorithm for multiclass classification.

A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full conditional independence between these two variables given all the other variables. In…

Method estimates joint probability density from samples using low-rank decomposition and random projections.

Quantum correlations enhance generative models, providing a new resource for machine learning.

A random walk $w_n$ on a separable, geodesic hyperbolic metric space $X$ converges to the boundary $\partial X$ with probability one when the step distribution supports two independent loxodromics. In particular, the random walk makes positive linear progress. Progress is known to be linear with exponential decay when …

This manuscript provides optimization guarantees, generalization bounds, and statistical consistency results for AdaBoost variants which replace the exponential loss with the logistic and similar losses (specifically, twice differentiable convex losses which are Lipschitz and tend to zero on one side). The heart of the…

A new Wasserstein $K$-means method for clustering probability distributions.

This work evaluates and improves calibration of probabilistic classifiers.

The paper simulates Lévy processes and their extremum and hitting time.

Reliable measures of statistical dependence could be useful tools for learning independent features and performing tasks like source separation using Independent Component Analysis (ICA). Unfortunately, many of such measures, like the mutual information, are hard to estimate and optimize directly. We propose to learn i…

The paper optimizes sample allocation for multiple distributions using various distance measures.

We consider composite loss functions for multiclass prediction comprising a proper (i.e., Fisher-consistent) loss over probability distributions and an inverse link function. We establish conditions for their (strong) convexity and explore the implications. We also show how the separation of concerns afforded by using …

Quantum computers outperform classical methods in density modeling.

Algorithm infers sampling distribution from i.i.d. samples without supervision.

Flexible copula model using implicit generative neural networks.

New algorithms estimate and test collision probability with near-optimal sample complexity.

In this note we prove the a pointwise ergodic theorem for functions taking values in a separable complete CAT(0)-space, analogous to Lindenstrauss' pointwise ergodic theorem for real-valued integrable functions on a probability space subject to a probability-preserving action of an amenable l.c.s.c. group, where in the…

A new method estimates rare events using tensor trains.

We study exact recovery conditions for convex relaxations of point cloud clustering problems, focusing on two of the most common optimization problems for unsupervised clustering: $k$-means and $k$-median clustering. Motivations for focusing on convex relaxations are: (a) they come with a certificate of optimality, and…

New decision-theoretic characterization separates belief and decision posteriors.

A new method combines classifiers using possibility distributions and adaptive t-norms.

SQFA learns features maximizing Fisher-Rao distance for better classification.