Related papers: INFO-SEDD: Continuous Time Markov Chains as Scalab…
Entropy governs molecular self-assembly, phase transitions, and material stability, yet remains challenging to quantify and directly control in molecular systems. Here, we demonstrate that the computable information density (CID), a data…
Continuous-time Markov chains are mathematical models that are used to describe the state-evolution of dynamical systems under stochastic uncertainty, and have found widespread applications in various fields. In order to make these models…
Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential…
We consider the task of learning a parametric Continuous Time Markov Chain (CTMC) sequence model without examples of sequences, where the training data consists entirely of aggregate steady-state statistics. Making the problem harder, we…
Markov models are often used to capture the temporal patterns of sequential data for statistical learning applications. While the Hidden Markov modeling-based learning mechanisms are well studied in literature, we analyze a…
Analyses of serially-sampled data often begin with the assumption that the observations represent discrete samples from a latent continuous-time stochastic process. The continuous-time Markov chain (CTMC) is one such generative model whose…
Inferring the infinitesimal rates of continuous-time Markov chains (CTMCs) is a central challenge in many scientific domains. This task is hindered by three factors: quadratic growth in the number of rates as the CTMC state space expands,…
Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the…
Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…
Information theoretic quantities play a central role in machine learning. The recent surge in the complexity of data and models has increased the demand for accurate estimation of these quantities. However, as the dimension grows the…
Computing the stationary distributions of a continuous-time Markov chain (CTMC) involves solving a set of linear equations. In most cases of interest, the number of equations is infinite or too large, and the equations cannot be solved…
Labeled continuous-time Markov chains (CTMCs) describe processes subject to random timing and partial observability. In applications such as runtime monitoring, we must incorporate past observations. The timing of these observations matters…
Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…
Stationary quantum information sources emit sequences of correlated qudits -- that is, structured quantum stochastic processes. If an observer performs identical measurements on a qudit sequence, the outcomes are a realization of a…
Information theoretic quantities play an important role in various settings in machine learning, including causality testing, structure inference in graphical models, time-series problems, feature selection as well as in providing privacy…
Discrete diffusion models based on continuous-time Markov chains (CTMCs) have shown strong performance on language and discrete data generation, yet existing approaches typically parameterize the reverse rate matrix monolithically --…
Discrete diffusion models have recently emerged as a powerful class of generative models for chemistry and biology data. In these fields, the goal is to generate various samples with high rewards (e.g., drug-likeness in molecules), making…
In this paper we present a novel method for estimating the parameters of a parametric diffusion processes. Our approach is based on a closed-form Maximum Likelihood estimator for an approximating Continuous Time Markov Chain (CTMC) of the…
Continuous diffusion models have demonstrated remarkable performance in data generation across various domains, yet their efficiency remains constrained by two critical limitations: (1) the local adjacency structure of the forward Markov…
Sequential data naturally arises from user engagement on digital platforms like social media, music streaming services, and web navigation, encapsulating evolving user preferences and behaviors through continuous information streams. A…