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Title: Metropolis Adjusted Underdamped Langevin Trajectories: a robust alternative to Hamiltonian Monte-Carlo

Abstract: Sampling approximations for high dimensional statistical models often rely on so-called gradient-based MCMC algorithms. It is now well established that these samplers scale better with the dimension than other state of the art MCMC samplers, but are also more sensitive to tuning [5]. Among these, Hamiltonian Monte Carlo is a widely used sampling method shown to achieve gold standard d^{1/4} scaling with respect to the dimension [1]. However it is also known that its efficiency is quite sensible to the choice of integration time, see e.g. [4], [2]. This problem is related to periodicity in the autocorrelations induced by the deterministic trajectories of Hamiltonian dynamics. To tackle this issue, we develop a robust alternative to HMC built upon underdamped Langevin (namely Metropolis Adjusted Underdamped Langevin Trajectories, or MAULT), inducing randomness in the trajectories through a continuous refreshment of the velocities. We study the optimal scaling problem for MAULT and recover the d^{1/4} scaling of HMC proven in [1] without additional assumptions. Furthermore we highlight the fact that autocorrelations for MAULT can be controlled by a uniform and monotonous bound thanks to the randomness induced in the trajectories, and therefore achieves robustness to tuning. Finally, we compare our approach to Randomized HMC ([2], [3]) and establish quantitative contraction rates for the 2-Wasserstein distance that support the choice of underdamped Langevin dynamics.

This is a joint work with Jure Vogrinc (University of Warwick)

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Presentation 1

Time: 11:00am – 11:30am

Speaker: Grace Yin, UBC Statistics MSc student

Title: On the Relationship between Predictive Models and Structural Causal Model Learning

Abstract: Structural Causal Models (SCMs) are a key component in causal inference and they have been used for a long time in many fields. We proposed an approach to identify the structure of an SCM based on a constant risk theorem. In particular, we proved that for an equivariant model and predictor, the risk function is constant across interventions described by the action of a group. These theories give a straightforward understanding of certain types of causal model identification. We also explored the risks on a specific SCM for linear regression predictive models with different types of interventions through simulation experiments.

Presentation 2

Time: 11:30am – 12:00pm

Speaker: Wei Tang, UBC Statistics MSc student

Title: Improved model training for multi-horizon time series forecasting in the context of COVID-19

Abstract: Predicting how the Covid-19 pandemic evolves in the future is very important for public health workers and policymakers to prepare for it. The prediction task is a multi-step time series forecasting task. In this report, we compared two commonly used strategies, the iterative and direct strategy, for this task on the Covid dataset under various experiment settings. We further enhanced the two strategies with ideas from K-Nearest Neighborhood (KNN) algorithm to construct the training dataset and proposed an improved iterative strategy which we call the dynamic iterative strategy. The proposed KNN enhanced forecasting strategies are significantly better than the native iterative and direct strategies and achieve satisfying prediction accuracy on the covid prediction challenge at the Covid-19 Forecasting Hub.

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Title: Bayesian Dose-Finding Design for Molecularly Targeted Agents and Immunotherapy

Abstract: Molecularly targeted agents and immunotherapy have revolutionized modern cancer treatment. Unlike chemotherapy, the maximum tolerated dose of the targeted therapies may not pose significant clinical benefit over the lower doses. By simultaneously considering both binary toxicity and efficacy endpoints, phase I/II trials can identify a better dose for subsequent phase II trials than traditional phase I trials in terms of efficacy-toxicity tradeoff. Existing phase I/II dose-finding methods are model-based or need to pre-specify many design parameters, which makes them difficult to implement in practice. To strengthen and simplify the current practice of phase I/II trials, we propose a utility-based toxicity probability interval (uTPI) design for finding the optimal biological dose (OBD) where binary toxicity and efficacy endpoints are observed. The uTPI design is model-assisted in nature, simply modeling the utility outcomes observed at the current dose level based on a quasibinomial likelihood. Toxicity probability intervals are used to screen out overly toxic dose levels, and then the dose escalation/de-escalation decisions are made adaptively by comparing the posterior utility distributions of the adjacent levels of the current dose. The uTPI design is flexible in accommodating various utility functions while only needing minimum design parameters. A prominent feature of the uTPI design is that it has a simple decision structure such that a concise dose-assignment decision table can be calculated before the start of the trial and be used throughout the trial, which greatly simplifies the practical implementation of the design. Extensive simulation studies demonstrate that the proposed uTPI design yields desirable as well as robust performance under various scenarios.

This talk is based on the joint work with Ruitao Lin and Ying Yuan at MD Anderson Cancer Center.

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Title: Stochastic Geometry for Machine Learning

Abstract: The Mondrian process in machine learning is a recursive partition of space with random axis-aligned cuts used to build random forests and Laplace kernel approximations. The construction allows for efficient online algorithms, but the restriction to axis-aligned cuts does not capture dependencies between features. By viewing the Mondrian as a special case of the stable under iterated (STIT) process in stochastic geometry, we resolve open questions about the generalization of cut directions. We utilize the theory of stationary random tessellations to show that STIT random features approximate a large class of stationary kernels and STIT random forests achieve minimax rates for Lipschitz and C^2 functions. This work opens many new questions at the intersection of stochastic geometry and machine learning. Based on joint work with Ngoc Tran.

Registration & talk details

This talk is one of Data Science Applied Research and Education Seminar (ARES) series. Learn more and register for this talk here.

Talk Title: Understanding animal movement with state-space models

Abstract: Movement data have become essential for our understanding of animal ecology. However, such data are associated with a broad range of challenges. For example, tracking the movement of many species (e.g. fish and small birds) is still limited to inaccurate technology, such as light-based geolocation. Making behavioral and spatial inferences based on such data is difficult because the tracks they create are not good representations of the animals’ movement. Understanding the behavior of animals using movement data is challenging even with accurate movement data, because we are often making inference on a process that is not observed directly. Through a set of examples from a broad range of animals (fish, bears, marine mammals), I will demonstrate how a state-space modeling framework can improve our understanding of animal movement.

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Abstract: MCMC methods are a popular tool in computation science used to evaluate expectations with respect to complex probability distributions over general state spaces. They work by averaging over the trajectory of a Markov chain stationary with respect to the target distribution. In theory, the MCMC algorithms converge asymptotically, but, in practice, for challenging problems where the target distributions are high-dimensional with well-separated modes, MCMC algorithms can get trapped exploring local regions of high probability and suffer from poor mixing.

Physicists and statisticians independently introduced parallel tempering (PT) algorithms to tackle this issue. PT delegates the task of exploration to additional annealed chains running in parallel with better mixing properties. They then communicate with the target chain of interest and help discover new unexplored regions of the sample space. Since their introduction in the 90s, PT algorithms are still extensively used to improve mixing in challenging sampling problems arising in statistics, physics, computational chemistry, phylogenetics, and machine learning.

The classical approach to designing PT algorithms was developed using a reversible paradigm that is difficult to tune and deteriorates in performance when too many parallel chains are introduced. This talk will introduce a new non-reversible paradigm for PT that dominates its reversible counterpart while avoiding the performance collapse endemic to reversible methods. We will then establish near-optimal tuning guidelines and efficient black-box methodology scalable to GPUs. Our work out-performs state-of-the-art PT methods and has been used at scale by researchers to study the evolutionary structure of cancer and discover magnetic polarization in the photograph of the supermassive black hole M87.

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Title: Doctor for AI: Prior-informed ML for Biomedical Imaging and Perception

Abstract: Deepening our understanding of human health is more important than ever before to address real-world challenges in biomedicine and healthcare, especially with the pandemic over recent years. My research focuses on AI in medicine, to develop efficient ML models for biomedical imaging and perception for addressing real-world challenges. In this talk, I will first explore the challenges in this emerging field and then present the two following lines of my work:

First, I will introduce my work in Doctor for AI: leverage the prior knowledge of doctors to design AI model for biomedical imaging. Specifically, I will discuss how to integrate different kinds of prior knowledge to develop reliable data-efficient ML models, by exploiting the personalized prior, population prior and physics prior. With the innovative ML models, the proposed approaches can be generally applied to various biomedical imaging applications including sparse-sampling image reconstruction, projection synthesis, and molecular imaging.

Second, I will introduce my work in AI for Doctor: develop ML-driven perception models that can adaptive to unique characteristics of biomedical data including random noise and multi-modality. Specifically, I will present a self-attention-guided ML model for quantitative image perception. Through international collaborations for cross-institute validation among four U.S. clinical centers and a Turkey institute, this work demonstrates the possibility for the developed ML model to characterize the in utero neurodevelopmental trajectory in real-world deployment.

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Title: What can statisticians learn from the analysis of C.elegans data?

Abstract: In modern scientific setups we are faced with unprecedented challenges regarding how to process data efficiently and in a robust way. These challenges often reveal the brittleness of our current tools, dictating the need for new methods. In this talk I will describe new statistical and AI methods motivated by a pressing problem in neuroscience, the need for imaging entire brains at single-neuron resolution.

Specifically, I will present my contribution to NeuroPAL, a new breakthrough technology that enables a colorful imaging of every single neuron in the brain of the C.elegans worm. I will describe new methods for two difficult tasks arising in these datasets: neural segmentation and identification. These two tasks are related to an underlying deconvolution model, a mixture of gaussians, and classical methods such as the EM algorithm fall short. Behind these new methods there is a key statistical physics principle, the so-called Schrödinger bridge, a ‘thought experiment’ that realizes the solution of an entropy-regularized optimal transport problem. This thought experiment was proposed in 1932 but it has yet to percolate into the mainstream of statistics.

I will first describe some fundamental statistical properties of the Schrödinger bridge that I established. For example, when estimating it from samples, it enjoys the 1/sqrt n convergence rate, avoiding the curse of dimensionality. Second, I will introduce a new loss function based on this principle and show that it is a better optimization objective than the log-likelihood for model-based clustering, reducing pathologies such as bad local optima and inconsistency. In consequence, a new algorithm derived from this loss, Sinkhorn EM, attains better, more robust neural segmentation performance. After, I will comment on how these principles can be used to probabilistically identify neurons in C.elegans, leading to meaningful uncertainty quantification on this hard combinatorial setup. Finally, I will comment on how these novel methods have proven to be useful in other contexts such as deep learning.

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Title: Bridging the Gap Between Deep Learning and Probabilistic Modeling

Abstract: Deep learning excels with large-scale unstructured data - common across many modern application domains - while probabilistic modeling offers the ability to encode prior knowledge and quantify uncertainty - necessary for safety-critical applications and downstream decision-making tasks. I will discuss examples from my research that bridge the gap between these two learning paradigms. The first half will show that insights from deep learning can improve the practicality of probabilistic models. I will discuss work that scales Gaussian process regression, a common probabilistic model, to datasets two orders of magnitude larger than previously reported. The second half will show that probabilistic methods can improve our understanding of deep learning. I will demonstrate that Gaussian process theory uncovers new insights about the effects of width and depth in neural networks. I will conclude with ongoing efforts to quantify neural network uncertainty, develop new inductive biases, and other work at the intersection of deep learning and probabilistic modeling.

Registration

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Abstract

One hopes that data analyses will be used to make beneficial decisions regarding people's health, finances, and well-being. But the data fed to an analysis may systematically differ from the data where these decisions are ultimately applied. For instance, suppose we analyze data in one country and conclude that microcredit is effective at alleviating poverty; based on this analysis, we decide to distribute microcredit in other locations and in future years. We might then ask: can we trust our conclusion to apply under new conditions? If we found that a very small percentage of the original data was instrumental in determining the original conclusion, we might expect the conclusion to be unstable under new conditions. So we propose a method to assess the sensitivity of data analyses to the removal of a very small fraction of the data set. Analyzing all possible data subsets of a certain size is computationally prohibitive, so we provide an approximation. We call our resulting method the Approximate Maximum Influence Perturbation. Our approximation is automatically computable, theoretically supported, and works for common estimators – including (but not limited to) OLS, IV, GMM, MLE, MAP, and variational Bayes. We show that any non-robustness our metric finds is conclusive. Empirics demonstrate that while some applications are robust, in others the sign of a treatment effect can be changed by dropping less than 0.1% of the data – even in simple models and even when standard errors are small.

van Eeden speakers

Professor Tamara Broderick 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.