arXiv research

Study distortion risk measures for step-weighted distributions.

W-Flow generates images in one step, faster and better than multi-step methods.

Simpler one-step distributional RL framework for control.

Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with step size compared to normal distribution. Thus it is essential to cut-off these di…

The paper extends risk measures to two-step approximations and studies log-concave distributions.

A recent algorithmic family for distributed optimization, DIGing's, have been shown to have geometric convergence over time-varying undirected/directed graphs. Nevertheless, an identical step-size for all agents is needed. In this paper, we study the convergence rates of the Adapt-Then-Combine (ATC) variation of the DI…

Distributed statistical inference has recently attracted enormous attention. Many existing work focuses on the averaging estimator. We propose a one-step approach to enhance a simple-averaging based distributed estimator. We derive the corresponding asymptotic properties of the newly proposed estimator. We find that th…

AutoStep MCMC adapts step size locally for better sampling efficiency.

Paper uses RL to optimize daily step distribution for better health biomarkers.

We consider $d$-dimensional linear stochastic approximation algorithms (LSAs) with a constant step-size and the so called Polyak-Ruppert (PR) averaging of iterates. LSAs are widely applied in machine learning and reinforcement learning (RL), where the aim is to compute an appropriate $θ_{*} \in \mathbb{R}^d$ (that is a…

Study optimizes step size for Metropolis algorithm in non-identifiable cases.

New algorithm for sampling from distributions with thin tails.

Eisenhart's theorem extended to sub-Riemannian metrics on specific Lie algebras.

The paper analyzes fixed step-size SA schemes on Riemannian manifolds.

Proposes an automatic cyclical scheduling for gradient-based discrete sampling.

In order to investigate the origin of large price fluctuations, we analyze stock price changes of ten frequently traded NASDAQ stocks in the year 2002. Though the influence of the trading frequency on the aggregate return in a certain time interval is important, it cannot alone explain the heavy tailed distribution of …

LocalKMeans parallelizes Lloyd's algorithm for distributed data.

EM Distillation simplifies diffusion models to one-step generators.

Continuous functions on graphs in Carnot groups satisfy a Burgers' type equation.

Paper presents a copula-based method to efficiently generate correlated sample paths from multi-step time series models.

Motivated by the geometric theory of differential equations and the variational approach to the equivalence problem for geometric structures on manifolds, we consider the problem of equivalence for distributions with fixed submanifolds of flags on each fiber. We call them flag structures. The construction of the canoni…

A new one-step method for covariate shift adaptation.

We investigate the statistics of records in a random sequence $\{x_B(0)=0,x_B(1),\cdots, x_B(n)=x_B(0)=0\}$ of $n$ time steps. The sequence $x_B(k)$'s represents the position at step $k$ of a random walk `bridge' of $n$ steps that starts and ends at the origin. At each step, the increment of the position is a random ju…

Optimal transport method rejects new classes and adjusts class ratios for open set domain adaptation.

Single-step samplers generate high-quality samples efficiently.

Quantized Stochastic Primal-Dual Methods for Distributed Optimization

Proposes a method combining CNFs and rejection-resampling for sampling from unnormalized densities.

Faster diffusion-based models generate data with fewer steps.

Local Gradient Descent with local steps converges to the centralized model in the interpolation regime.

This work proposes ACTC for adaptive distributed learning under communication constraints.

Delayed rejection HMC improves sampling efficiency for multiscale distributions.

RML improves generative modeling of complex distributions.

Paper improves CLT and bootstrap approximations for LSA with decreasing step size.

Graphical model learning and inference are often performed using Bayesian techniques. In particular, learning is usually performed in two separate steps. First, the graph structure is learned from the data; then the parameters of the model are estimated conditional on that graph structure. While the probability distrib…

New techniques improve distributed training with compressed gradients.

Lower bounds on MALA and HMC for well-conditioned distributions.

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 paper is a step-by-step tutorial for fitting a mixture distribution to data. It merely assumes the reader has the background of calculus and linear algebra. Other required background is briefly reviewed before explaining the main algorithm. In explaining the main algorithm, first, fitting a mixture of two distribu…

We present a novel approach for learning an HMM whose outputs are distributed according to a parametric family. This is done by {\em decoupling} the learning task into two steps: first estimating the output parameters, and then estimating the hidden states transition probabilities. The first step is accomplished by fit…

Existing uncertainty modeling approaches try to detect an out-of-distribution point from the in-distribution dataset. We extend this argument to detect finer-grained uncertainty that distinguishes between (a). certain points, (b). uncertain points but within the data distribution, and (c). out-of-distribution points. O…

SMT trains generative models by estimating mixture scores, outperforming existing methods.

LSDM uses unpaired data to match latent space distributions for generative modeling.

Unified framework for data-free sampling using Wasserstein gradient flows.

Model predicts stock price changes and forecasts using tokenized data.

The family of Expectation-Maximization (EM) algorithms provides a general approach to fitting flexible models for large and complex data. The expectation (E) step of EM-type algorithms is time-consuming in massive data applications because it requires multiple passes through the full data. We address this problem by pr…

ATLAS adapts HMC step size and trajectory length for complex geometries.

New approach shapes error distribution in long-term forecasting.

USD algorithm transports distributions with or without mass conservation.