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We introduce ImitationFlow, a novel Deep generative model that allows learning complex globally stable, stochastic, nonlinear dynamics. Our approach extends the Normalizing Flows framework to learn stable Stochastic Differential Equations.…
Recent years have seen advances in generalization bounds for noisy stochastic algorithms, especially stochastic gradient Langevin dynamics (SGLD) based on stability (Mou et al., 2018; Li et al., 2020) and information theoretic approaches…
Generalization of the Lorden's inequality is an excellent tool for obtaining strong upper bounds for the convergence rate for various complicated stochastic models. This paper demonstrates a method for obtaining such bounds for some…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing…
Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov transition operators provide explicit,…
Temporal point processes (TPPs) are a fundamental tool for modeling event sequences in continuous time, but most existing approaches rely on autoregressive parameterizations that are limited by their sequential sampling. Recent…
It has been shown \citep{broeck90:physicalreview,patarnello87:europhys} that feedforward Boolean networks can learn to perform specific simple tasks and generalize well if only a subset of the learning examples is provided for learning.…
We study the problem of efficient exploration in order to learn an accurate model of an environment, modeled as a Markov decision process (MDP). Efficient exploration in this problem requires the agent to identify the regions in which…
We study Bayesian inverse problems with mixed noise, modeled as a combination of additive and multiplicative Gaussian components. While traditional inference methods often assume fixed or known noise characteristics, real-world…
This paper introduces a novel methodology for the identification of switching dynamics for switched autoregressive linear models. Switching behavior is assumed to follow a Markov model. The system's outputs are contaminated by possibly…
Inspired by recent strides in empirical efficacy of implicit learning in many robotics tasks, we seek to understand the theoretical benefits of implicit formulations in the face of nearly discontinuous functions, common characteristics for…
In this document, we introduce a notion of entropy for stochastic processes on marked rooted graphs. For this, we employ the framework of local weak limit theory for sparse marked graphs, also known as the objective method, due to…
Transferring knowledge from one neural network to another has been shown to be helpful for learning tasks with few training examples. Prevailing fine-tuning methods could potentially contaminate pre-trained features by comparably high…
Ideas and formalisms from far-from-equilibrium thermodynamics are ported to the context of stochastic computational processes, via following and extending Tadaki's algorithmic thermodynamics. A Principle of Maximum Algorithmic Caliber is…
We derive new concentration bounds for time averages of measurement outcomes in quantum Markov processes. This generalizes well-known bounds for classical Markov chains which provide constraints on finite time fluctuations of time-additive…
The information-theoretic framework of Russo and J. Zou (2016) and Xu and Raginsky (2017) provides bounds on the generalization error of a learning algorithm in terms of the mutual information between the algorithm's output and the training…
We address the problem of community detection in networks by introducing a general definition of Markov stability, based on the difference between the probability fluxes of a Markov chain on the network at different time scales. The…
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…
We consider an agent trying to bring a system to an acceptable state by repeated probabilistic action. Several recent works on algorithmizations of the Lovasz Local Lemma (LLL) can be seen as establishing sufficient conditions for the agent…