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Generalizing manipulation skills to new situations requires extracting invariant patterns from demonstrations. For example, the robot needs to understand the demonstrations at a higher level while being invariant to the appearance of the…
The paper presents new asymptotic recurrent algorithms of phase space reduction for regularly and singularly perturbed semi-Markov processes. These algorithms give effective conditions of weak convergence for distributions and convergence…
In this paper we are looking for quantitative estimates for the convergene to equilibrium of non reversible Markov processes, especialy in short times. The models studied are simple enough to get an explicit expression of the L2 distance…
K. It\^{o} characterised in \cite{ito} zero-mean stationary Gauss Markov-processes evolving on a class of infinite-dimensional spaces. In this work we extend the work of It\^{o} in the case of Hilbert spaces: Gauss-Markov families that are…
Note that the serial structure of blockchain has many essential pitfalls, thus a data network structure and its DAG-based blockchain are introduced to resolve the blockchain pitfalls. From such a network perspective, analysis of the…
We introduce a novel generative framework for functions by integrating Implicit Neural Representations (INRs) and Transformer-based hypernetworks into latent variable models. Unlike prior approaches that rely on MLP-based hypernetworks with…
We have studied Markov processes on denumerable state space and continuous time. We found that all these processes are connected via gauge transformations. We have used this result before as a method for resolution of equations, included…
The two dominant approaches to neural text generation are fully autoregressive models, using serial beam search decoding, and non-autoregressive models, using parallel decoding with no output dependencies. This work proposes an…
The pseudo likelihood method of Besag(1974), has remained a popular method for estimating Markov random field on a very large lattice, despite various documented deficiencies. This is partly because it remains the only computationally…
The law of the iterated logarithm (LIL) for the time-homogeneous Markov process with a unique invariant measure characterizes the almost sure maximum possible fluctuation of time averages around the ergodic limit. Whether a numerical…
Autoregressive language models achieve remarkable performance, yet a unified theory explaining their internal mechanisms, how training shapes representations, and why these representations support complex behavior remains incomplete. We…
Attention-based transformers have achieved tremendous success across a variety of disciplines including natural languages. To deepen our understanding of their sequential modeling capabilities, there is a growing interest in using Markov…
We study time-changed Markov processes to speed up the convergence of Markov chain Monte Carlo (MCMC) algorithms. The time-changed process is defined by adjusting the speed of time of a base process via a user-chosen, state-dependent…
We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal categorical data. The main assumption behind these models is that the response variables are conditionally independent given a latent process…
Motivated by applications arising from sensor networks and machine learning, we consider the problem of minimizing a finite sum of nondifferentiable convex functions where each component function is associated with an agent and a…
Multi-type Markov point processes offer a flexible framework for modelling complex multi-type point patterns where it is pertinent to capture both interactions between points as well as large scale trends depending on observed covariates.…
We propose a new approach to inverse reinforcement learning (IRL) based on the deep Gaussian process (deep GP) model, which is capable of learning complicated reward structures with few demonstrations. Our model stacks multiple latent GP…
We introduce the minimal maximally predictive models ({\epsilon}-machines) of processes generated by certain hidden semi-Markov models. Their causal states are either hybrid discrete-continuous or continuous random variables and…
Lossy image compression is one of the most commonly used operators for digital images. Most recently proposed deep-learning-based image compression methods leverage the auto-encoder structure, and reach a series of promising results in this…
The zigzag process is a variant of the telegraph process with position dependent switching intensities. A characterization of the $L^2$-spectrum for the generator of the one-dimensional zigzag process is obtained in the case where the…