We analyze graph smoothing with mean aggregation, where each node successively
receives the average of the features of its neighbors. Indeed, it has quickly been observed …

This work considers a computationally and statistically efficient parameter estimation method
for a wide class of latent variable models—including Gaussian mixture models, hidden …

The vast majority of theoretical results in machine learning and statistics assume that the
training data is a reliable reflection of the phenomena to be learned. Similarly, most learning …

This book provides an introduction to the mathematical and algorithmic foundations of data
science, including machine learning, high-dimensional geometry, and analysis of large …

We design a new distribution over m× n matrices S so that, for any fixed n× d matrix A of rank
r, with probability at least 9/10,∥ SAx∥ 2=(1±ε)∥ Ax∥ 2 simultaneously for all x∈ R d …

We describe a general technique that yields the first Statistical Query lower bounds for a
range of fundamental high-dimensional learning problems involving Gaussian distributions …

Many real-world problems involve the optimization of multiple, possibly conflicting
objectives. Multi-objective reinforcement learning (MORL) is a generalization of standard …

Clustering data in high dimensions is believed to be a hard problem in general. A number of
efficient clustering algorithms developed in recent years address this problem by projecting …

Several results appeared that show significant reduction in time for matrix multiplication,
singular value decomposition as well as linear (lscr 2) regression, all based on data …

We use the Sum of Squares method to develop new efficient algorithms for learning well-
separated mixtures of Gaussians and robust mean estimation, both in high dimensions, that …