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Approximate message passing (AMP) emerges as an effective iterative paradigm for solving high-dimensional statistical problems. However, prior AMP theory -- which focused mostly on high-dimensional asymptotics -- fell short of predicting…
In order for robots and other artificial agents to efficiently learn to perform useful tasks defined by an end user, they must understand not only the goals of those tasks, but also the structure and dynamics of that user's environment.…
The Dynamical Gaussian Process Latent Variable Models provide an elegant non-parametric framework for learning the low dimensional representations of the high-dimensional time-series. Real world observational studies, however, are often…
We consider the problem of designing control laws for stochastic jump linear systems where the disturbances are drawn randomly from a finite sample space according to an unknown distribution, which is estimated from a finite sample of…
Most models of machine teaching and learning assume the learner makes no errors in its internal deductive inference. However, humans and large language models in few-shot learning regimes are two important examples of learners where this…
This paper studies the dynamic generator model for spatial-temporal processes such as dynamic textures and action sequences in video data. In this model, each time frame of the video sequence is generated by a generator model, which is a…
In this work, we study non-asymptotic bounds on correlation between two time realizations of stable linear systems with isotropic Gaussian noise. Consequently, via sampling from a sub-trajectory and using \emph{Talagrands'} inequality, we…
We explore unconstrained natural language feedback as a learning signal for artificial agents. Humans use rich and varied language to teach, yet most prior work on interactive learning from language assumes a particular form of input (e.g.,…
Sequential estimation of a vector of linear regression coefficients is considered under both centralized and decentralized setups. In sequential estimation, the number of observations used for estimation is determined by the observed…
We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models - sampling the posterior distribution over latent variables - is proposed to…
As data-driven methods are deployed in real-world settings, the processes that generate the observed data will often react to the decisions of the learner. For example, a data source may have some incentive for the algorithm to provide a…
Although stochastic approximation learning methods have been widely used in the machine learning literature for over 50 years, formal theoretical analyses of specific machine learning algorithms are less common because stochastic…
We study the problem of cooperative inference where a group of agents interact over a network and seek to estimate a joint parameter that best explains a set of observations. Agents do not know the network topology or the observations of…
In recent years, pre-trained large language models (LLMs) have demonstrated remarkable efficiency in achieving an inference-time few-shot learning capability known as in-context learning. However, existing literature has highlighted the…
This paper studies theory and inference related to a class of time series models that incorporates nonlinear dynamics. It is assumed that the observations follow a one-parameter exponential family of distributions given an accompanying…
Sequential learning -- where complex tasks are broken down into simpler, hierarchical components -- has emerged as a paradigm in AI. This paper views sequential learning through the lens of low-rank linear regression, focusing specifically…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
Strict stationarity is a common assumption used in the time series literature in order to derive asymptotic distributional results for second-order statistics, like sample autocovariances and sample autocorrelations. Focusing on weak…
The identification of nonlinear dynamics from observations is essential for the alignment of the theoretical ideas and experimental data. The last, in turn, is often corrupted by the side effects and noise of different natures, so…
Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…