Statistics and Probability Seminar Series

See also our calendar for a complete list of the Department of Mathematics and Statistics seminars and events.

Please email Guangqu ZHENG (gzheng90@bu.edu) if you would like to be added to the email list.

Fall 2025 Dates

(Time/location: Thursdays 4-5pm/CDS 365)

Sept. 18, Speaker: Lulu Kang (Umass Amherst)

Title: Building GP Surrogate Model with High-Dimensional Input
Abstract: Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation involves too many input variables. In this talk, I will present two different approaches to build Gaussian process surrogate model for experiments with high dimensional input. I first introduce an optimal kernel learning approach to identify the active variables, thereby overcoming GP model limitations and enhancing system understanding. This method approximates the original GP model’s covariance function through a convex combination of kernel functions, each utilizing low-dimensional subsets of input variables. The second approach is Bayesian bridge GP regression approach, in which we impose shrinkage penalty on the linear regression coefficients of the mean and correlation coefficients in the covariance function. This is equivalent to using certain proper informative priors on these parameters under Bayesian framework. Using Spherical Hamiltonian Monte Carlo, we can directly sample from the constrained posterior distribution without the restrictions on prior distribution as in Bayesian bridge regression.

Sept. 25, Speaker: Cheng Ouyang (University of Illinois at Chicago)

Title: Parabolic Anderson model on compact manifolds
Abstract: We introduce a family of intrinsic Gaussian noises on compact manifolds that we call “colored noise” on manifolds. With this noise, we study the parabolic Anderson model (PAM) on manifolds. Under some curvature conditions, we show the well-posedness of the PAM and provide some preliminary (but sharp) bounds on the second moment of the solution.

Oct. 2, Speaker: Nathan Ross (University of Melbourne)

Title: Gaussian random field approximation for wide neural networks
Abstract: It has been observed that wide neural networks (NNs) with randomly initialized weights may be well-approximated by Gaussian fields indexed by the input space of the NN, and taking values in the output space. There has been a flurry of recent work making this observation precise, since it sheds light on regimes where neural networks can perform effectively. In this talk, I will discuss recent work where we derive bounds on Gaussian random field approximation of wide random neural networks of any depth, assuming Lipschitz activation functions. The bounds are on a Wasserstein transport distance in function space equipped with a strong (supremum) metric, and are explicit in the widths of the layers and natural parameters such as moments of the weights. The result follows from a general approximation result using Stein’s method, combined with a novel Gaussian smoothing technique for random fields, which I will also describe. The talk covers joint works with Krishnakumar Balasubramanian, Larry Goldstein, and Adil Salim; and A.D. Barbour and Guangqu Zheng.

Oct. 9, Speaker: Konstantin Riedl (University of Oxford)

Title: Global Convergence of Adjoint-Optimized Neural PDEs
Abstract: Many engineering and scientific fields have recently become interested in modeling terms in partial differential equations (PDEs) with neural networks and solving the inverse problem of learning such terms from observed data in order to discover hidden physics. The resulting neural-network PDE model, being a function of the neural network parameters, can be calibrated to the available ground truth by optimizing over the PDE using gradient descent, where the gradient is evaluated in a computationally efficient manner by solving an adjoint PDE. These neural PDE models have emerged as an important research area in scientific machine learning. In this talk, we discuss the convergence of the adjoint gradient descent optimization method for training neural PDE models in the limit where both the number of hidden units and the training time tend to infinity. Specifically, for a general class of nonlinear parabolic PDEs with a neural network embedded in the source term, we prove convergence of the trained neural-network PDE solution to the target data (i.e., a global minimizer). The global convergence proof poses a unique mathematical challenge that is not encountered in finite-dimensional neural network convergence analyses due to (i) the neural network training dynamics involving a non-local neural network kernel operator in the infinite-width hidden layer limit where the kernel lacks a spectral gap for its eigenvalues and (ii) the nonlinearity of the limit PDE system, which leads to a non-convex optimization problem, even in the infinite-width hidden layer limit (unlike in typical neural network training cases where the optimization problem becomes convex in the large neuron limit). The theoretical results are illustrated and empirically validated by numerical studies. This talk is based on joint work with Justin Sirignano (University of Oxford) and Konstantinos Spiliopoulos (Boston University), see https://arxiv.org/abs/2506.13633 for the preprint.

Oct. 16, Speaker: Davar Khoshnevisan (University of Utah)

Title: On the passage times of self-similar Gaussian processes on curved boundaries
Abstract: PDF link (Oct16_2025)

Oct. 23, Speaker: Ian Stevenson (University of Connecticut)

Title: Statistical tools for modeling synapses and synaptic plasticity in large-scale spike recordings
Abstract: Synaptic plasticity underlies learning, memory, and recovery from injury. However, most of what is known about synapses is based on intracellular neural recordings in controlled, artificial conditions. In this talk, I’ll give an overview of progress we’ve made using statistical modeling to detect putative synapses and study synaptic plasticity in natural conditions in awake, behaving animals using data from large-scale extracellular spike recordings. Here we use biologically-inspired, dynamic generalized bilinear models to track short- and long-term synaptic changes. In experimental data, we find substantial changes in the weights of putative synapses at both fast (<1s) and slow (>1min) timescales. However, our modeling indicates that some apparent long-term fluctuations in synaptic strength may be byproducts of short-term plasticity. These results illustrate some of the ways that statistical modeling can generate insight into how and why neural circuits change over time.

Oct. 30, Speaker: Qiyang Han (Rutgers University)

Title: Algorithmic inference via nonconvex gradient descent
Abstract: Conventional statistical inference methods are typically developed for models simple enough to admit tractable estimators through carefully designed iterative algorithms. In contrast, modern deep learning models are enormously complex, yet are trained by simple gradient-descent–type algorithms, often without any provable guarantee of global optimality. Can we reconcile classical inference principles with these highly complicated, modern learning paradigms? In this talk, we present a new inference framework addressing this question. Conceptually, we show that valid statistical inference can be performed along the entire gradient descent trajectory, iteration by iteration, without requiring convexity of the loss landscape or convergence of the algorithm. To illustrate this concept, we begin with a single-index regression model and demonstrate how gradient descent iterates can be debiased, at each iteration, to yield valid confidence intervals for the underlying signal and consistent estimates of generalization errors. We then extend this paradigm to the much more challenging setting of learning with general multi-layer neural networks in their full complexity, where the loss landscape can be arbitrarily complex, yet our algorithmic inference method remains valid for each iteration. The key technical ingredient underlying this new inference paradigm is a recent entrywise dynamics theory for a broad class of first-order algorithms developed by the speaker.

Nov. 6, Speaker: Yimin Xiao (Michigan State University)

Title: Uniform Hausdorﬀ Dimension Results for Gaussian Random Fields and the Stochastic Heat Equations
Abstract: PDF link (nov6_2025)

Nov. 13, Speaker: Le Chen (Auburn University)

Title: Continuous random polymers in R^d
Abstract: I will present ongoing joint work with Cheng Ouyang, Samy Tindel, and Panqiu Xia on continuum random polymers in R^d. Motivated by discrete directed polymers and the one-dimensional continuum model driven by space–time white noise (Albert–Khanin–Quastel, 2014), we develop a higher-dimensional theory. In particular, we construct a polymer measure and study its canonical process X. We prove that X has Hölder-continuous paths and that its quadratic variation matches that of Brownian motion. Nevertheless, the resulting law is singular with respect to the standard Wiener measure on C([0,1]; R^d).

Nov. 20, Speaker: Igor Cialenco (Illinois Institute of Technology)

Title: Statistical analysis of discretely sampled SPDEs
Abstract:Unlike traditional finite-dimensional stochastic differential equations, statistical models driven by SPDEs are predominantly singular, when the solution is observed continuously on a finite time interval, yielding a reach class of statistical and stochastic analysis problems. After a brief discussion of some classical approaches to statistical inference for SPDEs, we will focus on (semilinear) parabolic SPDEs observed discretely in time or space in the physical domain. We prove a new central limit theorem for some power variations of the iterated integrals of a fractional Brownian motion (fBm), that consequently are used for the estimation of the drift and volatility coefficients of these equations. In particular, we show that naïve approximations of the solution or its derivates can introduce nontrivial biases that we compute explicitly.

Statistics and Probability Seminar Series

Statistics and Probability Seminar Series

Fall 2025 Dates

(Time/location: Thursdays 4-5pm/CDS 365)

Sept. 18, Speaker: Lulu Kang (Umass Amherst)

Sept. 25, Speaker: Cheng Ouyang (University of Illinois at Chicago)

Oct. 2, Speaker: Nathan Ross (University of Melbourne)

Oct. 9, Speaker: Konstantin Riedl (University of Oxford)

Oct. 16, Speaker: Davar Khoshnevisan (University of Utah)

Oct. 23, Speaker: Ian Stevenson (University of Connecticut)

Oct. 30, Speaker: Qiyang Han (Rutgers University)

Nov. 6, Speaker: Yimin Xiao (Michigan State University)

Nov. 13, Speaker: Le Chen (Auburn University)

Nov. 20, Speaker: Igor Cialenco (Illinois Institute of Technology)

Nov. 27, thanksgiving break

Dec. 4, TBA

Dec. 11, Speaker: Oanh Nguyen (Brown University)

Previous Speakers

Spring 2025

Yuchen Wu (University of Pennsylvania)

Ye Tian (Columbia University)

Charles Margossian (Flatiron Institute)

Yuetian Luo (University of Chicago)

Kai Tan (Rutgers University)

Anirban Chatterjee (University of Pennsylvania)

Georgia Papadogeorgou (University of Florida)

Murali Haran (Pennsylvania State University)

Yuguo Chen (University of Illinois at Urbana-Champaign)

Youssef Marzouk (MIT)

Yao Xie (Georgia Institute of Technology)

Andrea Rotnitzky (University of Washington)

Nabarun Deb (University of Chicago)

Jonathan Huggins (Boston University)

Fall 2024

Spring 2024

Fall 2023