arXiv research

New method adapts to unknown mixing time in stochastic optimization.

Proposes a method to allocate time budgets in mixed criticality systems.

MALA mixes optimally in κ√d steps for log-concave sampling.

Lower bound on BART's mixing time increases with data points.

MALA mixes efficiently under smoothness and isoperimetry assumptions.

In this article we discuss some of the consequences of the mixed membership perspective on time series analysis. In its most abstract form, a mixed membership model aims to associate an individual entity with some set of attributes based on a collection of observed data. Although much of the literature on mixed members…

The literature on statistical learning for time series assumes the asymptotic independence or ``mixing' of the data-generating process. These mixing assumptions are never tested, nor are there methods for estimating mixing rates from data. We give an estimator for the $β$-mixing rate based on a single stationary sample…

metabeta uses neural networks to speed up Bayesian mixed-effects regression.

We give a simple optimistic algorithm for which it is easy to derive regret bounds of $\tilde{O}(\sqrt{t_{\rm mix} SAT})$ after $T$ steps in uniformly ergodic Markov decision processes with $S$ states, $A$ actions, and mixing time parameter $t_{\rm mix}$. These bounds are the first regret bounds in the general, non-epi…

The paper analyzes convergence rates of Langevin dynamics and Proximal Sampler using $Φ$-divergence.

The study examines mixing times of data-augmentation Gibbs samplers for high-dimensional probit regression.

Paper analyzes Nyström regularization for time series forecasting with sequential sub-sampling.

In this short paper, in order to price occupation-time options, such as (double-barrier) step options and quantile options, we derive various joint distributions of a mixed-exponential jump-diffusion process and its occupation times of intervals.

Rapid mixing of Langevin dynamics on Riemannian manifolds

uHMC achieves fast mixing in high dimensions with gradient evaluations.

New framework improves multivariate time series forecasting by minimizing redundant information.

New method for conformal prediction under Markovian data reduces coverage gap.

New RL method MAC improves performance in sparse reward settings.

This paper resolves the Langevin Algorithm's mixing time for log-concave distributions.

Closed Riemannian manifolds with positive mixed sectional curvature

Many theoretical results on estimation of high dimensional time series require specifying an underlying data generating model (DGM). Instead, along the footsteps of~\cite{wong2017lasso}, this paper relies only on (strict) stationarity and $β$-mixing condition to establish consistency of lasso when data comes from a $β…

The paper develops new inequalities for Markov chain sums, linking them to mixing time.

The paper develops methods to derive mixed superposition rules for Lie systems and applies them to various physical systems.

We propose and analyze two new MCMC sampling algorithms, the Vaidya walk and the John walk, for generating samples from the uniform distribution over a polytope. Both random walks are sampling algorithms derived from interior point methods. The former is based on volumetric-logarithmic barrier introduced by Vaidya wher…

Improves meta-learning efficiency with mixed-mode differentiation.

New method improves sampling from logconcave distributions truncated on polytopes.

NUTS mixing time scales as d^(1/4) for Gaussian distributions.

The study uses Hidden Markov Models to analyze student enrollment patterns and academic performance.

This work improves mixing rates for Bayesian CART, a key component of BART.

The aim of this paper is to evaluate geometric Asian option by a mixed fractional subdiffusive Black-Scholes model. We derive a pricing formula for geometric Asian option when the underlying stock follows a time changed mixed fractional Brownian motion. We then apply the results to price Asian power options on the stoc…

A new unsupervised contrastive learning framework improves time series representation learning.

Accurate predictions of reactive mixing are critical for many Earth and environmental science problems. To investigate mixing dynamics over time under different scenarios, a high-fidelity, finite-element-based numerical model is built to solve the fast, irreversible bimolecular reaction-diffusion equations to simulate …

New algorithm for sampling from distributions with thin tails.

We derive and analyze learning algorithms for apprenticeship learning, policy evaluation, and policy gradient for average reward criteria. Existing algorithms explicitly require an upper bound on the mixing time. In contrast, we build on ideas from Markov chain theory and derive sampling algorithms that do not require …

We study probability measures induced by set functions with constraints. Such measures arise in a variety of real-world settings, where prior knowledge, resource limitations, or other pragmatic considerations impose constraints. We consider the task of rapidly sampling from such constrained measures, and develop fast M…

We address the problem of estimating the mixing time of a Markov chain from a single trajectory of observations. Unlike most previous works which employed Hilbert space methods to estimate spectral gaps, we opt for an approach based on contraction with respect to total variation. Specifically, we estimate the contracti…

Improved lower bound for parallel tempering's mixing time.

We introduce a novel multivariate random process producing Bernoulli outputs per dimension, that can possibly formalize binary interactions in various graphical structures and can be used to model opinion dynamics, epidemics, financial and biological time series data, etc. We call this a Bernoulli Autoregressive Proces…

This paper compares two NUTS variants and analyzes their convergence and mixing times.

This article provides the first procedure for computing a fully data-dependent interval that traps the mixing time $t_{\text{mix}}$ of a finite reversible ergodic Markov chain at a prescribed confidence level. The interval is computed from a single finite-length sample path from the Markov chain, and does not require t…

Hamiltonian Monte Carlo (HMC) is a state-of-the-art Markov chain Monte Carlo sampling algorithm for drawing samples from smooth probability densities over continuous spaces. We study the variant most widely used in practice, Metropolized HMC with the Störmer-Verlet or leapfrog integrator, and make two primary contribut…

New bounds for mixing time and privacy in projected Langevin algorithm and noisy SGD.

New algorithm learns optimal policy for average reward MDPs with sample complexity matching lower bound.

Paper uses machine learning for nowcasting corporate earnings from mixed-frequency data.

Method generates i.i.d. samples from GT data using space-time mixing.

Solves Christoffel-Minkowski problem for axially symmetric bodies.

This work analyzes Gibbs samplers for Bayesian hierarchical models without dimensionality constraints.

We prove that the ordinary least-squares (OLS) estimator attains nearly minimax optimal performance for the identification of linear dynamical systems from a single observed trajectory. Our upper bound relies on a generalization of Mendelson's small-ball method to dependent data, eschewing the use of standard mixing-ti…