arXiv research

Transformers can learn Markov processes with constant depth, surprising results.

Transformers with multiple layers learn to estimate bigram distributions, while single-layer models often get stuck in unigram local minima.

This paper studies transformer learning dynamics and initialization.

MLDL preserves manifold geometry in vector transformations.

Solves optimal stopping for Gauss-Markov bridges using time-space transformation.

Cai, Song and Kou (2015) [Cai, N., Y. Song, S. Kou (2015) A general framework for pricing Asian options under Markov processes. Oper. Res. 63(3): 540-554] made a breakthrough by proposing a general framework for pricing both discretely and continuously monitored Asian options under one-dimensional Markov processes. In …

Improves MCMC performance with adaptive affine transformations.

This paper precisely estimates transformer derivatives for explicit learning guarantees.

This paper develops tools for nonreversible MCMC with convergence guarantees.

Novel CMG framework improves financial sentiment forecasting.

This work proposes an efficient autoregressive model for text generation.

DNFS trains efficient samplers for discrete distributions using locally equivariant Transformers.

ST-BCP narrows the coverage gap in BCP by transforming nonconformity scores.

LLMs are compared to Markov chains for natural language processing.

The study explains how transformer components enable in-context learning.

Variance plays a crucial role in risk-sensitive reinforcement learning, and most risk measures can be analyzed via variance. In this paper, we consider two law-invariant risks as examples: mean-variance risk and exponential utility risk. With the aid of the state-augmentation transformation (SAT), we show that, the two…

Transformers learn causal structure through gradient descent on self-attention mechanisms.

New methods reduce computational cost for Gaussian Markov Random Fields with sparse constraints.

SwISS improves scalability of Bayesian inference for large datasets.

Prior work inspired by compression algorithms has described how the Burrows Wheeler Transform can be used to create a distance measure for bioinformatics problems. We describe issues with this approach that were not widely known, and introduce our new Burrows Wheeler Markov Distance (BWMD) as an alternative. The BWMD a…

Predicts next item in sequential bundles using Transformers.

Characterizes Bayesian networks up to unconditional equivalence.

We address the problem of parameter estimation for diffusion driven stochastic volatility models through Markov chain Monte Carlo (MCMC). To avoid degeneracy issues we introduce an innovative reparametrisation defined through transformations that operate on the time scale of the diffusion. A novel MCMC scheme which ove…

Extends Gaussian process regression for non-Gaussian data.

We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use techniques from optimal transport to select optimal such maps. Optimal transport theory a…

Mixtures of Gaussians, factor analyzers (probabilistic PCA) and hidden Markov models are staples of static and dynamic data modeling and image and video modeling in particular. We show how topographic transformations in the input, such as translation and shearing in images, can be accounted for in these models by inclu…

We propose a Las Vegas transformation of Markov Chain Monte Carlo (MCMC) estimators of Restricted Boltzmann Machines (RBMs). We denote our approach Markov Chain Las Vegas (MCLV). MCLV gives statistical guarantees in exchange for random running times. MCLV uses a stopping set built from the training data and has maximum…

In many state-of-the-art compression systems, signal transformation is an integral part of the encoding and decoding process, where transforms provide compact representations for the signals of interest. This paper introduces a class of transforms called graph-based transforms (GBTs) for video compression, and proposes…

Efficiently infers coupled hidden Markov models with noisy discrete observations.

A new model for time series using discrete latent states.

SAHMM-VAE separates sources adaptively using hidden Markov priors.

Study on financial systems using perturbed unimodal maps with heteroscedastic noise.

We introduce a new algorithm for approximate inference that combines reparametrization, Markov chain Monte Carlo and variational methods. We construct a very flexible implicit variational distribution synthesized by an arbitrary Markov chain Monte Carlo operation and a deterministic transformation that can be optimized…

There is an increasing demand for computing the relevant structures, equilibria and long-timescale kinetics of biomolecular processes, such as protein-drug binding, from high-throughput molecular dynamics simulations. Current methods employ transformation of simulated coordinates into structural features, dimension red…

Method estimates number of clusters in Block Markov Chain trajectories.

Paper tackles action delays in reinforcement learning, proposing a delay-aware framework.

Develops a model for bid and ask prices using stochastic control.

Markov Chain Monte Carlo methods become increasingly popular in applied mathematics as a tool for numerical integration with respect to complex and high-dimensional distributions. However, application of MCMC methods to heavy tailed distributions and distributions with analytically intractable densities turns out to be…

Bayesian model for discrete data with conditional transformations.

Unified approach to denoising Markov models for efficient sampling.

This paper investigates optimal portfolio strategies in a market where the drift is driven by an unobserved Markov chain. Information on the state of this chain is obtained from stock prices and expert opinions in the form of signals at random discrete time points. As in Frey et al. (2012), Int. J. Theor. Appl. Finance…

New Q-learning method achieves optimal sample complexity for average-reward problems.

Transformers learn to integrate information from past positions incrementally, specializing heads in distinct patterns.

Transformers learn to make decisions in new contexts from offline data.

Transformers prefer simpler explanations in hierarchical tasks.

This work extends identifiability analysis to sequential latent variable models, focusing on Switching Dynamical Systems.

This paper offers a simple method for Bayesian regression with unknown transformations.

Local mappings relate dual and primal factor graphs for efficient marginal probability estimation.