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Hawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, neuroscience and many other…

Terrorist activities often exhibit temporal and spatial clustering, making the multivariate Hawkes process (MHP) a useful statistical model for analysing terrorism across different geographic regions. However, terror attack data from the…

Assessing the synergistic high-order behaviors (HOBs) that emerge from underlying structural mechanisms is crucial to characterize complex systems. This work leverages the combined use of predictability and information measures to detect…

We study a multivariate, non-linear Hawkes process $Z^N$ on the complete graph with $N$ nodes. Each vertex is either excitatory (probability $p$) or inhibitory (probability $1-p$). We take the mean-field limit of $Z^N$, leading to a…

We introduce Multi-Environment Markov Decision Processes (MEMDPs) which are MDPs with a set of probabilistic transition functions. The goal in a MEMDP is to synthesize a single controller with guaranteed performances against all…

In this paper, we study semiparametric inference for linear multivariate Hawkes processes, a class of point processes widely used to describe self and mutually exciting phenomena. We establish a convolution theorem giving the best limiting…

In this paper, we present a nonparametric estimation procedure for the multivariate Hawkes point process. The timeline is cut into bins and -- for each component process -- the number of points in each bin is counted. The distribution of…

We present a machine learning approach for model-independent new physics searches. The corresponding algorithm is powered by recent large-scale implementations of kernel methods, nonparametric learning algorithms that can approximate any…

We propose a scalable semiparametric Bayesian model to capture dependencies among multiple neurons by detecting their co-firing (possibly with some lag time) patterns over time. After discretizing time so there is at most one spike at each…

We prove a central limit type theorem for critical marked Hawkes processes. We study the case where the marks are i.i.d. with nonnegative values and their common distribution is either heavy tailed or has finite variance. The kernel…

Let $\mathscr{P}(E)$ be the space of probability measures on a measurable space $(E,\mathcal{E})$. In this paper we introduce a class of nonlinear Markov chain Monte Carlo (MCMC) methods for simulating from a probability measure…

Sample-efficient exploration is crucial not only for discovering rewarding experiences but also for adapting to environment changes in a task-agnostic fashion. A principled treatment of the problem of optimal input synthesis for system…

We establish a scalable manifold learning method and theory, motivated by the problem of estimating fMRI activation manifolds in the Human Connectome Project (HCP). Our primary contribution is the development of an efficient estimation…

Machine learning interatomic potentials (MLIPs) enable efficient molecular dynamics (MD) simulations with ab initio accuracy and have been applied across various domains in physical science. However, their performance often relies on…

We propose a new class of learning algorithms that combines variational approximation and Markov chain Monte Carlo (MCMC) simulation. Naive algorithms that use the variational approximation as proposal distribution can perform poorly…

Social media conversations unfold based on complex interactions between users, topics and time. While recent models have been proposed to capture network strengths between users, users' topical preferences and temporal patterns between…

Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time.…

Effectively modeling non-stationary dynamics in probabilistic multivariate time series(MTS) forecasting requires balancing expressiveness with robustness. Existing parametric approaches benefit from strong inductive biases but lack…

We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…

In many specific scenarios, accurate and effective system identification is a commonly encountered challenge in the model predictive control (MPC) formulation. As a consequence, the overall system performance could be significantly weakened…