http://www-math.umd.edu/research/seminars.html http://www-math.umd.edu/research/seminars.html Tue, 26 Sep 2023 04:00:00 EDT Where: Kirwan Hall 0102
Speaker: Amandeep Chanda (University of Maryland College Park) -

]]> http://www-math.umd.edu/research/seminars.html Thu, 01 Feb 2024 15:30:00 EST Where: Kirwan Hall 1310
Speaker: Jane-Ling Wang (University of California-Davis) - https://anson.ucdavis.edu/~wang/
Abstract: Unlike standard tasks, survival analysis requires modeling incomplete data, such as right-censored data, which must be treated with care. While deep neural networks excel in traditional supervised learning, it remains unclear how to best utilize these models in survival analysis. A key question asks which data-generating assumptions of traditional survival models should be retained and which should be made more flexible via the function-approximating capabilities of neural networks.  In addition, most of these methods are difficult to interpret and mathematical understanding of them is lacking. In this talk, we explore these issues from two directions. First, we study the partially linear Cox model, where the nonlinear component of the model is implemented using a deep neural network. The proposed approach is flexible and able to circumvent the curse of dimensionality, yet it facilitates interpretability of the effects of treatment covariates on survival.  Next, we introduce a Deep Extended Hazard (DeepEH) model to provide a flexible and general framework for deep survival analysis. The extended hazard model includes the conventional Cox proportional hazards  and accelerated failure time models as special cases, so DeepEH subsumes the popular Deep Cox proportional hazard (DeepSurv) and Deep Accelerated Failure Time (DeepAFT) models.  We provide theoretical support for the proposed models, which underscores the attractive feature that deep learning is able to detect low-dimensional structure of data in high-dimensional space.  Numerical experiments further provide evidence that the proposed methods outperform existing statistical and deep learning approaches to survival analysis.  

*Based on Joint work with Qixian Zhong (Xiamen University) and Jonas Mueller (Clean Lab)

]]> http://www-math.umd.edu/research/seminars.html Thu, 04 Apr 2024 15:30:00 EDT Where: Kirwan 1310
Speaker: Emma Jingfei Zhang (Emory University ) - https://sites.google.com/view/ejzhang
Abstract: Recent advances in data collection technology have multiplied the availability of network data, leading to not only larger and more complex networks but also to instances where independent network samples are collected. In such data sets, a network serves as the basic data object, and they are increasingly common in neuroscience and genetics. When analyzing these data, a fundamental scientific question of interest is to understand how the subject-level network connectivity changes as a function of clinical characteristics. In this talk, we propose a new network response model framework, in which the networks are treated as responses and the network-level covariates as predictors. Under the proposed framework, we discuss model identifiability, estimation and theoretical properties. Finally, we present our findings from the analyses of three resting-state and task-related neuroimaging studies.  
]]> http://www-math.umd.edu/research/seminars.html Thu, 11 Apr 2024 15:30:00 EDT Where: Kirwan 1310
Speaker: Yixin Wang (University of Michigan) - https://yixinwang.github.io
Abstract:
Representation learning constructs low-dimensional representations to
summarize essential features of high-dimensional data like images and
texts. Ideally, such a representation should efficiently capture
non-spurious features of the data. It shall also be disentangled so
that we can interpret what feature each of its dimensions captures.
However, these desiderata are often intuitively defined and
challenging to quantify or enforce.

In this talk, we take on a causal perspective of representation
learning. We show how desiderata of representation learning can be
formalized using counterfactual notions, enabling metrics and
algorithms that target efficient, non-spurious, and disentangled
representations of data. We discuss the theoretical underpinnings of
the algorithm and illustrate its empirical performance in both
supervised and unsupervised representation learning.

This is joint work with Kartik Ahuja, Yoshua Bengio, Michael Jordan,
Divyat Mahajan, and Amin Mansouri:
https://arxiv.org/abs/2109.03795
https://arxiv.org/abs/2209.11924
https://arxiv.org/abs/2310.02854
]]> http://www-math.umd.edu/research/seminars.html Thu, 18 Apr 2024 15:30:00 EDT Where: Kirwan 1310
Speaker: Keith Levin (University of Wisconsin) - https://pages.stat.wisc.edu/~kdlevin/
Abstract: Network autoregressive models seek to model peer effects such as contagion and interference, in which node-level responses or behaviors may influence one another. These models are frequently deployed by practitioners in sociology and econometrics, typically in the form of linear-in-means models, in which node-level covariates and local averages of responses are used as predictors. In highly structured networks, previous work has shown that peer effects in linear-in-means models are colinear with other regression terms, and thus cannot be estimated, but this collinearity is widely believed to be ignorable, as peer effects are typically identified in empirical networks. In this work, we show a concerning negative result: under linear-in-means models, when node-level covariates are independent of network structure, peer effects become increasingly collinear with other regression terms as the network size (i.e., number of nodes) grows, and are inestimable asymptotically. We also show a narrow positive result: under certain latent space network models, some peer effects remain identified as the network size grows, albeit under rather stringent conditions. Our results suggest that linear models for peer effects are appropriate in far fewer settings than was previously believed.
]]> http://www-math.umd.edu/research/seminars.html Thu, 25 Apr 2024 15:30:00 EDT Where: Kirwan 1310
Speaker: Dimitris N. Politis (University of California-San Diego) - https://mathweb.ucsd.edu/~politis/
Abstract: Predictive inference under a general regression setting is gaining more interest in the
big-data era. In terms of going beyond point prediction to develop prediction intervals, two
main threads of development are Conformal Prediction and Model-free Prediction. Recently,
Chernozhukov et al. [2021] proposed a new conformal prediction approach exploiting the same uniformization procedure as in the Model-free Bootstrap of Politis [2015]. Hence, it is of interest to compare and further investigate the performance of the two methods. In the paper at hand, we contrast the two approaches via theoretical analysis and numerical experiments with a focus on conditional coverage of prediction intervals. We discuss suitable scenarios for applying each algorithm, underscore the importance of conditional vs. unconditional coverage, and show that, under mild conditions, the Model-free bootstrap yields prediction intervals with guaranteed better conditional coverage compared to quantile estimation. We also extend the concept of ‘pertinence’ of prediction intervals in Politis [2015] to the nonparametric regression setting, and give concrete examples where its importance emerges under finite sample scenarios. Finally, we define the new notion of ‘conjecture testing’ that is the analog of hypothesis testing as
applied to the prediction problem.

]]> http://www-math.umd.edu/research/seminars.html Thu, 02 May 2024 15:30:00 EDT Where: Kirwan 1310
Speaker: Malay Ghosh (The University of Florida ) -
Abstract: The Inverse-Wishart (IW) distribution is a standard and popular choice of priors for covariance matrices and has attractive properties such as conditional conjugacy. However, the IW family of priors has crucial drawbacks, including the lack of effective choices for non-informative priors. Several classes of priors for covariance matrices
that alleviate these drawbacks, while preserving computational tractability, have been proposed in the literature. These priors can be obtained through appropriate scale mixtures of IW priors. However, the high-dimensional posterior consistency of models which incorporate such priors has not been investigated. We address this issue for
the multi-response regression setting ( q responses,  n samples) under a wide variety of IW scale mixture priors for the error covariance matrix. Posterior consistency and contraction rates for both the regression coefficient matrix and the error covariance matrix are established in the "large q , large n " setting under mild assumptions on the
true data-generating covariance matrix and relevant hyperparameters. In particular, the number of responses q=q_n is allowed to grow with n , but with q_n = o(n). Also, some results related to the inconsistency of the posterior are provided.
]]> http://www-math.umd.edu/research/seminars.html Tue, 07 May 2024 15:30:00 EDT Where: Math 1310
Speaker: Michael Zhang (The University of Hong Kong ) - https://michaelzhang01.github.io
Abstract: The Gaussian process latent variable model (GPLVM) is a popular probabilistic method used for nonlinear dimension reduction, matrix factorization, and state-space modeling. Inference for GPLVMs is computationally tractable only when the data likelihood is Gaussian. Moreover, inference for GPLVMs has typically been restricted to obtaining maximum a posteriori point estimates, which can lead to overfitting, or variational approximations, which mischaracterize the posterior uncertainty. Here, we present a method to perform Markov chain Monte Carlo (MCMC) inference for generalized Bayesian nonlinear latent variable modeling. The crucial insight necessary to generalize GPLVMs to arbitrary observation models is that we approximate the kernel function in the Gaussian process mappings with random Fourier features; this allows us to compute the gradient of the posterior in closed form with respect to the latent variables. We show that we can generalize GPLVMs to non-Gaussian observations, such as Poisson, negative binomial, and multinomial distributions, using our random feature latent variable model (RFLVM). Our generalized RFLVMs perform on par with state-of-the-art latent variable models on a wide range of applications, including motion capture, images, and text data for the purpose of estimating the latent structure and imputing the missing data of these complex data sets.
]]> http://www-math.umd.edu/research/seminars.html Thu, 09 May 2024 15:30:00 EDT Where: Math 1310
Speaker: Didong Li (University of North Carolina-Chapel Hill ) - https://sites.google.com/view/didongli/
Abstract: Spatial data pervades numerous fields, ranging from geospatial research to genomics and image analysis, typically within a 2-dimensional plane. Gaussian Processes (GPs) have become foundational in studying these datasets. However, the conventional approach often centers solely on the function. This talk revisits the historical essence of calculus, championed by Newton and Leibniz, and extends it to the novel territory of Gaussian Processes. We commence with the derivative and curvature processes derived from Gaussian Processes, known as the ‘derivative process’ and the ‘curvature process’, and their pivotal role in spatial omics data—a burgeoning domain in genomics. Transitioning to non-Euclidean domains, intrinsic to studies of surfaces such as the brain, heart, and teeth, we outline the recent advancements of GPs in these manifold domains. Through a rigorous definition of the associated derivative and curvature processes, we provide a blueprint of the conditions required for their existence and derive their joint distributions for comprehensive statistical inference. This talk, thus, traces the journey of the derivative concept, bridging its historical significance with modern applications in spatial data analysis.
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