Related papers: Variable Length Memory Chains: characterization of…

We study the problem of learning the Markov order in categorical sequences that represent paths in a network, i.e. sequences of variable lengths where transitions between states are constrained to a known graph. Such data pose challenges…

This paper presents a distributed learning model predictive control (DLMPC) scheme for distributed linear time invariant systems with coupled dynamics and state constraints. The proposed solution method is based on an online distributed…

Can autoregressive large language models (LLMs) learn consistent probability distributions when trained on sequences in different token orders? We prove formally that for any well-defined probability distribution, sequence perplexity is…

Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is…

Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity…

Markov Chain Monte Carlo (MCMC) methods for sampling probability density functions (combined with abundant computational resources) have transformed the sciences, especially in performing probabilistic inferences, or fitting models to data.…

Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory…

We consider refined versions of Markov chains related to juggling introduced by Warrington. We further generalize the construction to juggling with arbitrary heights as well as infinitely many balls, which are expressed more succinctly in…

This paper considers continuous-time block-monotone Markov chains (BMMCs) and their block-augmented truncations. We first introduce the block monotonicity and block-wise dominance relation for continuous-time Markov chains, and then provide…

Bayesian phylogenetic inference is often conducted via local or sequential search over topologies and branch lengths using algorithms such as random-walk Markov chain Monte Carlo (MCMC) or Combinatorial Sequential Monte Carlo (CSMC).…

Large language models (LLMs) have demonstrated impressive performance on reasoning tasks, including mathematical reasoning. However, the current evaluation mostly focuses on carefully constructed benchmarks and neglects the consideration of…

We study the properties of a subclass of stochastic processes called discrete time nonlinear Markov chains with an aggregator, which naturally appear in various topics such as strategic queueing systems, inventory dynamics, opinion…

In this paper, we introduce variational semantic memory into meta-learning to acquire long-term knowledge for few-shot learning. The variational semantic memory accrues and stores semantic information for the probabilistic inference of…

We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on…

Sampling a random permutation with restricted positions, or equivalently approximating the permanent of a 0-1 matrix, is a fundamental problem in computer science, with several notable results achieved over the years. However, existing…

We consider the problem of estimating the measure of subsets in very large networks. A prime tool for this purpose is the Markov Chain Monte Carlo (MCMC) algorithm. This algorithm, while extremely useful in many cases, still often suffers…

This paper studies three kinds of long-term behaviours, namely reachability, repeated reachability and persistence, of quantum Markov chains (qMCs). As a stepping-stone, we introduce the notion of bottom strongly connected component (BSCC)…

Most successful applications of deep learning involve similar training and test conditions. However, tasks such as biological sequence design involve searching for sequences that improve desirable properties beyond previously known values,…

The article studies segmentation problem (also known as classification problem) with pairwise Markov models (PMMs). A PMM is a process where the observation process and underlying state sequence form a two-dimensional Markov chain, it is a…

Heavy-tailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closed-form in graphical models which involve such heavy-tailed distributions. In this work, we…