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Presentation 1

Time: 11:00am – 11:30am

Speaker: Jiayang Yin, UBC Statistics MSc student

Title: On the Improvement of Density Ratio Estimation – Theoretical Study and Its Applications

Abstract: Density ratio estimation is an effective tool in the world of machine learning and data science, especially in transfer learning and contrastive learning. By contrastive learning, it is also linked to intractable likelihood and un-normalized model inference. Our work mainly focuses on a type of density ratio estimation based on a probabilistic classification from the perspective of statistical inference. We study how such a density ratio estimation relates to a probabilistic classifier such as Logistic regression. We analyze the potential cause for its inefficiency and inaccuracy when the two distributions are much different from each other. Opposite to the target of a probabilistic classification, a density ratio estimation task with a more efficient estimator indicates the corresponding classification task is harder, which means it is more difficult to separate the two samples by a probabilistic classifier. We provide a theoretical explanation for this phenomenon from a mathematical and statistical standpoint. For the basic density ratio estimation by a probabilistic classification, we give a necessary and sufficient condition for its existence under a sample level. We analyze the probability with such conditions held asymptotically. Besides, we explore the asymptotic properties of a recent proposed approach to improving density ratio estimation by a probabilistic classification – Telescoping Density Ratio Estimation TDRE by Rhodes, et al. Numerically, we compare the asymptotic variance of basic density ratio estimation and TDRE. We also explore some generalization on TDRE with unbalanced data and under some model misspecification by both theoretical discussion and empirical analysis. Based on our work, some suggestions for future work on un-normalized model inference are also provided.

Presentation 2

Time: 11:30am – 12:00pm

Speaker: Jintong Yan, UBC Statistics MSc student

Title: Biostatistical Analysis of Biomarker Discovery in Two Chronic Diseases

Abstract: Exploring biomarkers, such as DNA sequencing, RNA sequencing, and protein data, that may be correlated with a specific disease can help guide its treatment and diagnosis. During my co-op at PROOF Centre, I worked on multiple projects with a focus on two: using Somalogic protein profiling to explore early diagnosis of acute rheumatic fever from plasma, and developing biomarkers to guide immunosuppression strategies during cytomegalovirus (CMV) infection in heart transplant patients. The main objective of this presentation is to demonstrate how statistics can be used in these two projects to help identify biomarkers that can be used for diagnosing or treating diseases.

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Title: AI-Driven Experimental Design for Accelerating Science and Engineering

Abstract: AI-driven experimental design methods have the potential to accelerate costly discovery and optimization tasks throughout science and engineering—from materials design and drug discovery to computer systems tuning and instrument control. These methods are promising as they provide the intelligent decision making needed for use in complex real-world problems where experiments are time-consuming or expensive, and efficiency is paramount. In the first part of my talk, I will discuss challenges that I encountered while applying these methods to new types of scientific optimization problems being pursued at national labs. I will then introduce an information-based framework for flexible experimental design, which overcomes these challenges by enabling easy customization to new problem settings. This framework is theoretically principled, and has been used by scientists for efficient materials synthesis and optimization in large scientific instruments. Along the way, I will discuss my vision for reliable systems that expand the scope of AI-driven experimental design and make it easier to use, so that it can be put in the hands of scientists, engineers, and other practitioners everywhere.

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Title: Optimal methods for reinforcement learning: Efficient algorithms with instance-dependent guarantees

Abstract: Reinforcement learning (RL) is a pillar for modern artificial intelligence and data-driven decision making. Compared to classical statistical learning, several new statistical phenomena arise from RL problems, leading to different trade-offs in the choice of the estimators, tuning of their parameters, and the design of computational algorithms. In many settings, asymptotic and/or worst-case theory fails to provide the relevant guidance.

In this talk, I present recent advances in optimal algorithms for reinforcement learning. The bulk of this talk focuses on function approximation methods for policy evaluation. I establish a novel class of optimal and instance-dependent oracle inequalities for projected Bellman equations, as well as efficient computational algorithms achieving them under different settings. Among other results, I will highlight how the instance-dependent guarantees guide the selection of tuning parameters in temporal different methods. Drawing on this perspective, I will also discuss a novel class of stochastic approximation methods, yielding optimal statistical guarantees for solving the Bellman optimality equation. At the end of this talk, I will discuss additional works on optimal and instance-dependent guarantees for functional estimation with off-policy data.

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Abstract: Inferring the causal relationship between a treatment and a response is complicated in non-randomized studies owing to the effects of potentially confounding variables. Extensive work has been conducted to account for the effects of such variables in statistical analyses. However, previous works have demonstrated that misspecifying the set of potential confounders can have significant consequences for causal effect estimation. Bayesian Adjustment for Confounders (BAC) is a Bayesian approach to variable selection, whereby a mixture of posteriors is used to combine the causal effect estimates from each model corresponding to a combination of the potential confounders. Our work uses Monte Carlo simulation techniques in order to estimate the inflation in the average mean squared error due to prior misspecification in the BAC methodology over repeated experiments in a saturated probability model case study. Our findings shed light on future areas for research, and provide users of the BAC methodology with advice on selecting an appropriate prior model for their studies.

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Title: Statistically efficient offline reinforcement learning

Abstract: Despite the empirical success of reinforcement learning (RL) in gaming, such as for AlphaGo and OpenAI Five, we have not seen this level of successful application of RL in many scientific domains. This is because running experiments involving human interaction is often costly and risky. Thus, statistically efficient offline RL (i.e., sequential decision-making in a sample-efficient manner using offline data) is key to solving this limitation. In this talk, I will showcase my research on statistically efficient offline RL. Mostly, I will explain our unified “double minimax RL framework” for offline policy evaluation, which satisfies several desiderata such as (1) it can integrate any rich function approximation such as deep neural networks, (2) it is statistically efficient (i.e., attaining the semiparametric efficiency bound). For the remainder of the time, I will discuss model-based offline RL with general function approximation. I present a new algorithm named constrained pessimistic policy optimization (CPPO) to address the most challenging problem in offline RL known as “distributional shift,” which occurs when the offline data coverage is not sufficient. Our CPPO algorithm is able to learn high-quality policies even if the coverage of offline data is not sufficient.

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Title: Statistical and computational phenomena in deep learning

Abstract: Deep learning's success has revealed a number of phenomena that appear to conflict with classical intuitions in the fields of optimization and statistics.  First, the objective functions formulated in deep learning are highly nonconvex but are typically amenable to minimization with first-order optimization methods like gradient descent.  And second, neural networks trained by gradient descent are capable of 'benign overfitting': they can achieve zero training error on noisy training data and simultaneously generalize well to unseen data.  In this talk we go over our recent work towards understanding these phenomena.  We show how the framework of proxy convexity allows for tractable optimization analysis despite nonconvexity, while the implicit regularization of gradient descent plays a key role in benign overfitting.   In closing, we discuss some of the questions that motivate our current work on understanding deep learning, and how we may use our insights to make deep learning more trustworthy, efficient, and powerful.

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Title: Adversarial Bayesian Simulation

Abstract: In the absence of explicit or tractable likelihoods, Bayesians often resort to approximate Bayesian computation (ABC) for inference. Our work bridges ABC with deep neural implicit samplers based on generative adversarial networks (GANs) and adversarial variational Bayes. Both ABC and GANs compare aspects of observed and fake data to simulate from posteriors and likelihoods, respectively. We develop a Bayesian GAN (B-GAN) sampler that directly targets the posterior by solving an adversarial optimization problem. B-GAN is driven by a deterministic mapping learned on the ABC reference by conditional GANs. Once the mapping has been trained, iid posterior samples are obtained by filtering noise at a negligible additional cost. We propose two post-processing local refinements using (1) data-driven proposals with importance reweighting, and (2) variational Bayes. We support our findings with frequentist-Bayesian results, showing that the typical total variation distance between the true and approximate posteriors converges to zero for certain neural network generators and discriminators. Our findings on simulated data show highly competitive performance relative to some of the most recent likelihood-free posterior simulators.

Registration

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Title

The four pillars of machine learning

Abstract

I will present a unified perspective on the field of machine learning research, following the structure of my recent book, "Probabilistic Machine Learning: Advanced Topics" (https://probml.github.io/book2). In particular, I will discuss various models and algorithms for tackling the following four key tasks, which I call the "pillars of ML": prediction, control, discovery and generation. For each of these tasks, I will also briefly summarize a few of my own contributions, including methods for robust prediction under distribution shift, statistically efficient online decision making, discovering hidden regimes in high-dimensional time series data, and for generating high-resolution images.

van Eeden speakers

Dr. Kevin Patrick Murphy has been invited by our department's graduate students to be this year's van Eeden speaker. A van Eeden speaker is a prominent statistician who is chosen by our graduate students each year to give a lecture, supported by the Constance van Eeden Fund.

This seminar is sponsored by Canadian Statistical Sciences Institute (CANSSI).

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Abstract: Approaches systematically characterizing interactions via transcriptomic data usually follow two systems: (1) co-expression network analyses focusing on correlations between genes; (2) linear regressions (usually regularized) to select multiple genes jointly. Both suffer from the problem of stability: a slight change of parameterization or dataset could lead to dramatic alternations of outcomes. Here, we propose Stabilized Core gene and Pathway Election, or SCOPE, a tool integrating bootstrapped LASSO and co-expression analysis, leading to robust outcomes insensitive to variations in data. By applying SCOPE to six cancer expression datasets (BRCA, COAD, KIRC, LUAD, PRAD and THCA) in The Cancer Genome Atlas, we identified core genes capturing interaction effects in crucial pan-cancer pathways related to genome instability and DNA damage response. Moreover, we highlighted the pivotal role of CD63 as an oncogenic driver and a potential therapeutic target in kidney cancer. SCOPE enables stabilized investigations towards complex interactions using transcriptome data.

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Abstract: Cancer arises and evolves through the accumulation of somatic mutations which may provide a selective advantage. The interplay of mutations and their functional consequences shapes tumor progression and contributes to different clinical outcomes. Single-cell sequencing data enables a high-resolution characterization of this process, but requires powerful statistical models able to distinguish signal from noise. In this talk I discuss computational methods to analyze single-cell sequencing data from tumors to reconstruct the evolution of cancer cells, map genomic to transcriptional changes, and characterize the complex cell type composition of the tumor microenvironment. We present novel statistical models to integrate single-cell transcriptomes with copy number evolutionary trees, and to find hierarchical gene signatures from single-cell RNA-sequencing data. These methods provide rich descriptions of intra-tumor heterogeneity which are fundamental for the understanding of its complex dynamics and the development of targeted therapies.