Within high-dimensional genomic data, including genetic markers, complex phenotypes, and gene expression measurements, hides a substantial amount of low dimensional structure. In order to extract this low dimensional structure from high dimensional data, latent factor models with appropriate priors and modeling assumptions can be applied. A key advantage of sparse latent factor models in genomic applications is interpretability: the low dimensional structure can often be understood in a biological context. Model specification here is important, however, as genomics data generally includes small numbers of samples n with respect to enormous numbers of features p. Sparse linear latent factor models have been used to identify population substructure. Applying these models to high dimensional noisy phenotypes produces interpretable phenotypes that can subsequently tested for association with genetic variants. This same idea can be considered for gene expression traits, where the low dimensional structure captures groups of interacting genes, and the associated genetic variants represent master regulators. In this talk, I will discuss recent work on sparse latent factor models, and results on genomic data.
Having long been recognized in combinatorics, the concept of submodularity is becoming increasingly important in machine learning, since it can capture intuitive and yet non-trivial interactions between variables. This expressiveness has found many applications in machine learning, particularly in understanding structured data like text, vision and speech. Submodular functions naturally capture aspects of information, coverage and diversity in maximization problems, while also modelling notions of cooperation, sparsity, complexity and economies of scale in minimization problems. In this talk, we shall consider a large class of submodular optimization problems and motivate them with several real world applications, particularly in machine learning. We shall then provide a unifying algorithmic framework for solving several of these optimization problems, and highlight the scalability and practicality of this approach. We willl also highlight novel theoretical characterizations, which provide better connections between theory and practice. We shall ground this entire talk with a large number of applications in machine learning, including image segmentation, image correspondence, image collection summarization, feature selection, and data subset selection. This talk should be self contained and shall not require prior knowledge of submodular functions and optimization.
(this is based on joint work with Jeff Bilmes, Stefanie Jegelka, Sebastian Tschiatschek and Kai Wei)
A major challenge for machine learning in the next decade is the development of methods that continuously predict and learn from a stream of data. The scale of data and the non-stationary nature of the environment make the prevalent ``learn from a batch of i.i.d. data'' paradigm of Statistical Learning inadequate. Despite the extensive literature on sequential prediction (online learning) methods, the theoretical understanding of the subject has been lacking, and the results have been obtained on a case-by-case basis. This stands in contrast to Statistical Learning, where the inherent complexities have been well-understood in the last forty years. In this talk, we focus on no-regret online learning and develop the relevant notions of complexity in a surprising parallel to Statistical Learning Theory. This non-constructive study of inherent complexity is then augmented with a recipe for developing efficient online learning algorithms via a notion of a relaxation. To demonstrate the utility of our approach, we develop a new family of randomized methods, as well as new algorithms for collaborative filtering and node prediction.
Latent variable models have become a key tool for the modern statistician, letting us express complex assumptions about the hidden structures that underlie our data. Latent variable models have been successfully applied in numerous fields including natural language processing, computer vision, electronic medical records, genetics, neuroscience, astronomy, political science, sociology, the digital humanities, and many others.
The central computational problem in latent variable modeling is posterior inference, the problem of approximating the conditional distribution of the latent variables given the observations. Posterior inference is central to both exploratory tasks, where we investigate hidden structures that underlie our data, and predictive tasks, where we use the inferred structures to generalize about future data. Approximate posterior inference algorithms have revolutionized Bayesian statistics, revealing its potential as a usable and general-purpose language for data analysis.
Bayesian statistics, however, has not yet reached this potential. First, statisticians and scientists regularly encounter massive data sets, but existing approximate inference algorithms do not scale well. Second, most approximate inference algorithms are not generic; each must be adapted to the specific model at hand. This often requires significant model-specific analysis, which precludes us from easily exploring a variety of models.
In this talk I will discuss our recent research on addressing these two limitations. First I will describe stochastic variational inference, an approximate inference algorithm for handling massive data sets. Stochastic inference is easily applied to a large class of Bayesian models, including time-series models, factor models, and Bayesian nonparametric models. I will demonstrate its application to probabilistic topic models of text conditioned on millions of articles. Stochastic inference opens the door to scalable Bayesian computation for modern data analysis.
Then I will discuss black box variational inference. Black box inference is a generic algorithm for approximating the posterior. We can easily apply it to many models with little model-specific derivation and few restrictions on their properties. Black box inference performs better than similarly generic sampling algorithms, such as Metropolis-Hastings inside Gibbs, and can be composed with stochastic inference to handle massive data. I will demonstrate its use on a suite of nonconjugate models of longitudinal healthcare data.
This is joint work based on these two papers:
M. Hoffman, D. Blei, J. Paisley, and C. Wang. Stochastic variational inference. Journal of Machine Learning Research, 14:1303-1347.
R. Ranganath and D. Blei. Black box variational inference. Artificial Intelligence and Statistics, 2014.
There is a growing scientific interest in simultaneously estimating the means (or effect-sizes) of many different features. Classical (but very unintuitive) results in Stein-estimation show that even if these features are independent, cleverly coupling their mean estimates can greatly improve estimation accuracy. These ideas have been extended to build locally adaptive estimators based on perspectives from non-parametric empirical Bayesian estimation (and compound decision theory). Unfortunately, these estimators are not simple, and are really only tractable in highly idealized scenarios.
In recent work, we introduce a different framework for this estimation problem. Our framework is intuitive and shows how estimates from "independent features" become coupled through selection bias. We also give a simple general estimator based on resampling which is applicable and performs well in a wide variety of scenarios.
In this talk I will discuss the intuition behind "coupling estimates from independent features." I will review empirical Bayes/Stein Estimation, and I will introduce our framework. I will explain the connections between these estimators, show how they compare in practice.
This presentation is intended for a general machine learning audience.
This is joint work with Richard Simon (NIH) and recently Kean Ming Tan and Daniela Witten (UW) with occasional skepticism from Brad Efron (Stanford).
In recent years, with the advancement of large-scale data acquisition technology in various engineering, scientific and socio-economical domains, traditional machine learning and statistical methods have started to struggle with massive amounts of increasingly high-dimensional data. Luckily, in many problems there is a simple structure underlying high-dimensional data that can be exploited to make learning feasible.
In this talk, I will focus on the problem of detection and localization of a contiguous block of weak activation in a large matrix, from a small number of noisy, possibly adaptive, compressive measurements. This is closely related to the problem of compressed sensing, where the task is to estimate a sparse vector using a small number of linear measurements. Contrary to results in compressed sensing, where it has been shown that neither adaptivity nor contiguous structure help much, we show that for reliable localization the magnitude of the weakest signals is strongly influenced by both structure and the ability to choose measurements adaptively while for detection neither adaptivity nor structure reduce the requirement on the magnitude of the signal. We characterize the precise tradeoffs between the various problem parameters, the signal strength and the number of measurements required to reliably detect and localize the block of activation. The sufficient conditions are complemented with information theoretic lower bounds.
Joint work with Sivaraman Balakrishnan, Alessandro Rinaldo and Aarti Singh.
Peer grading serves as a critical tool for scaling the grading of complex, open-ended assignments to courses with tens or hundreds of thousands of students. But despite promising initial trials, it does not always deliver accurate results compared to human experts. I will talk about methods for estimating and correcting for grader biases and reliabilities, showing significant improvement in peer grading accuracy on real data with 63,199 peer grades from Coursera's HCI course offerings --- the largest peer grading networks analyzed to date. I will also discuss the relationship between grader biases and reliabilities to other student factors such as student engagement, performance as well as commenting style.
I will also discuss scalable feedback in the context of coding assignments, which have more structure than arbitrary open ended assignments. I outline a novel way to decompose online coding submissions into a vocabulary of “code phrases”. Based on this vocabulary, we have architected a queryable index that allows fast searches into the massive dataset of student homework submissions. To demonstrate the utility of our homework search engine we index over a million code submissions from users worldwide in Stanford’s Machine Learning massive open online course (MOOC) and then (a) semi-automatically learn shared structure amongst homework submissions and (b) generate specific feedback for student mistakes.
This is joint work with Chris Piech, Andy Nguyen, Zhenghao Chen, Chuong Do, Andrew Ng, Daphne Koller and Leonidas Guibas
Joint work with Raman Arora (TTI-C), Nicolo Cesa-Bianchi (Milano), Jian Ding (UChicago), Tomer Koren (Technion), Yuval Peres (MSR), Ohad Shamir (Weizmann), and Ambuj Tewari (UMICH)
The talk is intended for a general machine learning audience.