Aaditya Ramdas

Simultaneously uncovering the patterns of brain regions involved in different story reading subprocesses

Story understanding involves many perceptual and cognitive subprocesses, from perceiving individual words, to parsing sentences, to understanding the relationships among the story characters. We present an integrated computational model of reading that incorporates these and additional subprocesses, simultaneously discovering their fMRI signatures. Our model predicts the fMRI activity associated with reading arbitrary text passages, well enough to distinguish which of two story segments is being read with 74% accuracy. This approach is the first to simultaneously track diverse reading subprocesses during complex story processing and predict the detailed neural representation of diverse story features, ranging from visual word properties to the mention of different story characters and different actions they perform. We construct brain representation maps that replicate many results from a wide range of classical studies that focus each on one aspect of language processing and offer new insights on which type of information is processed by different areas involved in language processing. Additionally, this approach is promising for studying individual differences: it can be used to create single subject maps that may potentially be used to measure reading comprehension and diagnose reading disorders.

Fast and Flexible ADMM Algorithms for Trend Filtering

This article presents a fast and robust algorithm for trend filtering, a recently developed nonparametric regression tool. It has been shown that, for estimating functions whose derivatives are of bounded variation, trend filtering achieves the minimax optimal error rate, while other popular methods like smoothing splines and kernels do not. Standing in the way of a more widespread practical adoption, however, is a lack of scalable and numerically stable algorithms for fitting trend filtering estimates. This article presents a highly efficient, specialized alternating direction method of multipliers (ADMM) routine for trend filtering. Our algorithm is competitive with the specialized interior point methods that are currently in use, and yet is far more numerically robust. Furthermore, the proposed ADMM implementation is very simple, and, importantly, it is flexible enough to extend to many interesting related problems, such as sparse trend filtering and isotonic trend filtering. Software for our method is freely available, in both the C and R languages.

Convergence Properties of the Randomized Extended Gauss--Seidel and Kaczmarz Methods

The Kaczmarz and Gauss-Seidel methods both solve a linear system

Algorithmic Connections between Active Learning and Stochastic Convex Optimization

\bf{X}\bf{\beta} = \bf{y}

Rows versus Columns: Randomized Kaczmarz or Gauss--Seidel for Ridge Regression

by iteratively refining the solution estimate. Recent interest in these methods has been sparked by a proof of Strohmer and Vershynin which shows the randomized Kaczmarz method converges linearly in expectation to the solution. Lewis and Leventhal then proved a similar result for the randomized Gauss-Seidel algorithm. However, the behavior of both methods depends heavily on whether the system is under or overdetermined, and whether it is consistent or not. Here we provide a unified theory of both methods, their variants for these different settings, and draw connections between both approaches. In doing so, we also provide a proof that an extended version of randomized Gauss-Seidel converges linearly to the least norm solution in the underdetermined case (where the usual randomized Gauss Seidel fails to converge). We detail analytically and empirically the convergence properties of both methods and their extended variants in all possible system settings. With this result, a complete and rigorous theory of both methods is furnished.

Decoding from pooled data: Phase transitions of message passing

Interesting theoretical associations have been established by recent papers between the fields of active learning and stochastic convex optimization due to the common role of feedback in sequential querying mechanisms. In this paper, we continue this thread in two parts by exploiting these relations for the first time to yield novel algorithms in both fields, further motivating the study of their intersection. First, inspired by a recent optimization algorithm that was adaptive to unknown uniform convexity parameters, we present a new active learning algorithm for one-dimensional thresholds that can yield minimax rates by adapting to unknown noise parameters. Next, we show that one can perform

Regularized brain reading with shrinkage and smoothing

d

Iterative Methods for Solving Factorized Linear Systems

-dimensional stochastic minimization of smooth uniformly convex functions when only granted oracle access to noisy gradient signs along any coordinate instead of real-valued gradients, by using a simple randomized coordinate descent procedure where each line search can be solved by

Minimax lower bounds for linear independence testing

1

Towards a deeper geometric, analytic and algorithmic understanding of margins

-dimensional active learning, provably achieving the same error convergence rate as having the entire real-valued gradient. Combining these two parts yields an algorithm that solves stochastic convex optimization of uniformly convex and smooth functions using only noisy gradient signs by repeatedly performing active learning, achieves optimal rates and is adaptive to all unknown convexity and smoothness parameters.