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Estimating frequencies of elements appearing in a data stream is a key task in large-scale data analysis. Popular sketching approaches to this problem (e.g., CountMin and CountSketch) come with worst-case guarantees that probabilistically…

The application of standard sufficient dimension reduction methods for reducing the dimension space of predictors without losing regression information requires inverting the covariance matrix of the predictors. This has posed a number of…

Over the past few years, the multi-armed bandit model has become increasingly popular in the machine learning community, partly because of applications including online content optimization. This paper reviews two different sequential…

It is often necessary to make sampling-based statistical inference about many probability distributions in parallel. Given a finite computational resource, this article addresses how to optimally divide sampling effort between the samplers…

This paper presents the first convergence result for random search algorithms to a subset of the Pareto set of given maximum size k with bounds on the approximation quality. The core of the algorithm is a new selection criterion based on a…

Value-based reinforcement-learning algorithms have shown strong results in games, robotics, and other real-world applications. Overestimation bias is a known threat to those algorithms and can sometimes lead to dramatic performance…

We propose a new weighted average estimator for the high dimensional parameters under the distributed learning system, in which the weight assigned to each coordinate is precisely proportional to the inverse of the variance of the local…

We show that a large class of Estimation of Distribution Algorithms, including, but not limited to, Covariance Matrix Adaption, can be written as a Monte Carlo Expectation-Maximization algorithm, and as exact EM in the limit of infinite…

We give algorithms for estimating the expectation of a given real-valued function $\phi:X\to {\bf R}$ on a sample drawn randomly from some unknown distribution $D$ over domain $X$, namely ${\bf E}_{{\bf x}\sim D}[\phi({\bf x})]$. Our…

Margin has played an important role on the design and analysis of learning algorithms during the past years, mostly working with the maximization of the minimum margin. Recent years have witnessed the increasing empirical studies on the…

Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…

An automatic machine learning (AutoML) task is to select the best algorithm and its hyper-parameters simultaneously. Previously, the hyper-parameters of all algorithms are joint as a single search space, which is not only huge but also…

Information divergence that measures the difference between two nonnegative matrices or tensors has found its use in a variety of machine learning problems. Examples are Nonnegative Matrix/Tensor Factorization, Stochastic Neighbor…

A lot of real-world engineering problems represent dynamicity with nests of nonlinearities due to highly complex network of exponential functions or large number of differential equations interacting together. Such search spaces are…

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…

In many real-world scenarios involving high-stakes and safety implications, a human decision-maker (HDM) may receive recommendations from an artificial intelligence while holding the ultimate responsibility of making decisions. In this…

We introduce the Meta Highly-Adaptive-Lasso Minimum Loss Estimator (M-HAL-MLE), a novel ensemble approach for estimating functional parameters of realistically modeled data distribution from independent and identically distributed…

Gibbs-ERM learning is a natural idealized model of learning with stochastic optimization algorithms (such as Stochastic Gradient Langevin Dynamics and ---to some extent--- Stochastic Gradient Descent), while it also arises in other…

The classical center based clustering problems such as $k$-means/median/center assume that the optimal clusters satisfy the locality property that the points in the same cluster are close to each other. A number of clustering problems arise…

This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates…