The quality of K-Means clustering is extremely sensitive to proper initialization. The classic remedy is to apply k-means++ to obtain an initial set of centers that is provably competitive with the optimal solution. Unfortunately, k-means++ requires k full passes over the data which limits its applicability to massive datasets. We address this problem by proposing a simple and efficient seeding algorithm for K-Means clustering. The main idea is to replace the exact D2-sampling step in k-means++ with a substantially faster approximation based on Markov Chain Monte Carlo sampling. We prove that, under natural assumptions on the data, the proposed algorithm retains the full theoretical guarantees of k-means++ while its computational complexity is only sublinear in the number of data points. For such datasets, one can thus obtain a provably good clustering in sublinear time. Extensive experiments confirm that the proposed method is competitive with k-means++ on a variety of real-world, large-scale datasets while offering a reduction in runtime of several orders of magnitude.

Many planning methods rely on the use of an immediate reward function as a portable and succinct representation of desired behavior. Rewards are often inferred from demonstrated behavior that is assumed to be near-optimal. We examine a framework, Distance Minimization IRL (DM-IRL), for learning reward functions from scores an expert assigns to possibly suboptimal demonstrations. By changing the expert’s role from a demonstrator to a judge, DM-IRL relaxes some of the assumptions present in IRL, enabling learning from the scoring of arbitrary demonstration trajectories with unknown transition functions. DM-IRL complements existing IRL approaches by addressing different assumptions about the expert. We show that DM-IRL is robust to expert scoring error and prove that finding a policy that produces maximally informative trajectories for an expert to score is strongly NP-hard. Experimentally, we demonstrate that the reward function DM-IRL learns from an MDP with an unknown transition model can transfer to an agent with known characteristics in a novel environment, and we achieve successful learning with limited available training data.

Kernel Principal Component Analysis (PCA) is a popular extension of PCA which is able to find nonlinear patterns from data. However, the application of kernel PCA to large-scale problems remains a big challenge, due to its quadratic space complexity and cubic time complexity in the number of examples. To address this limitation, we utilize techniques from stochastic optimization to solve kernel PCA with linear space and time complexities per iteration. Specifically, we formulate it as a stochastic composite optimization problem, where a nuclear norm regularizer is introduced to promote low-rankness, and then develop a simple algorithm based on stochastic proximal gradient descent. During the optimization process, the proposed algorithm always maintains a low-rank factorization of iterates that can be conveniently held in memory. Compared to previous iterative approaches, a remarkable property of our algorithm is that it is equipped with an explicit rate of convergence. Theoretical analysis shows that the solution of our algorithm converges to the optimal one at an O(1/T) rate, where T is the number of iterations.

This paper addresses the problem of active learning of a multi-output Gaussian process (MOGP) model representing multiple types of coexisting correlated environmental phenomena. In contrast to existing works, our active learning problem involves selecting not just the most informative sampling locations to be observed but also the types of measurements at each selected location for minimizing the predictive uncertainty (i.e., posterior joint entropy) of a target phenomenon of interest given a sampling budget. Unfortunately, such an entropy criterion scales poorly in the numbers of candidate sampling locations and selected observations when optimized. To resolve this issue, we first exploit a structure common to sparse MOGP models for deriving a novel active learning criterion. Then, we exploit a relaxed form of submodularity property of our new criterion for devising a polynomial-time approximation algorithm that guarantees a constant-factor approximation of that achieved by the optimal set of selected observations. Empirical evaluation on real-world datasets shows that our proposed approach outperforms existing algorithms for active learning of MOGP and single-output GP models.

Pose-based action recognition in 3D is the task of recognizing an action (e.g., walking or running) from a sequence of 3D skeletal poses. This is challenging because of variations due to different ways of performing the same action and inaccuracies in the estimation of the skeletal poses. The training data is usually small and hence complex classifiers risk over-fitting the data. We address this task by action-snippets which are short sequences of consecutive skeletal poses capturing the temporal relationships between poses in an action. We propose a novel representation for action-snippets, called activated simplices. Each activity is represented by a manifold which is approximated by an arrangement of activated simplices. A sequence (of action-snippets) is classified by selecting the closest manifold and outputting the corresponding activity. This is a simple classifier which helps avoid over-fitting the data but which significantly outperforms state-of-the-art methods on standard benchmarks.

Hierarchical latent tree analysis (HLTA) is recently proposed as a new method for topic detection. It differs fundamentally from the LDA-based methods in terms of topic definition, topic-document relationship, and learning method. It has been shown to discover significantly more coherent topics and better topic hierarchies. However, HLTA relies on the Expectation-Maximization (EM) algorithm for parameter estimation and hence is not efficient enough to deal with large datasets. In this paper, we propose a method to drastically speed up HLTA using a technique inspired by the advances in the method of moments. Empirical experiments show that our method greatly improves the efficiency of HLTA. It is as efficient as the state-of-the-art LDA-based method for hierarchical topic detection and finds substantially better topics and topic hierarchies.

Despite decades of effort to combat spam, unwanted and even malicious emails, such as phish which aim to deceive recipients into disclosing sensitive information, still routinely find their way into one's mailbox.To be sure, email filters manage to stop a large fraction of spam emails from ever reaching users, but spammers and phishers have mastered the art of filter evasion, or manipulating the content of email messages to avoid being filtered.We present a unique behavioral experiment designed to study email filter evasion.Our experiment is framed in somewhat broader terms: given the widespread use of machine learning methods for distinguishing spam and non-spam, we investigate how human subjects manipulate a spam template to evade a classification-based filter.We find that adding a small amount of noise to a filter significantly reduces the ability of subjects to evade it, observing that noise does not merely have a short-term impact, but also degrades evasion performance in the longer term.Moreover, we find that greater coverage of an email template by the classifier (filter) features significantly increases the difficulty of evading it.This observation suggests that aggressive feature reduction — a common practice in applied machine learning — can actually facilitate evasion.In addition to the descriptive analysis of behavior, we develop a synthetic model of human evasion behavior which closely matches observed behavior and effectively replicates experimental findings in simulation.

Graph-based clustering methods perform clustering on a fixed input data graph. If this initial construction is of low quality then the resulting clustering may also be of low quality. Moreover, existing graph-based clustering methods require post-processing on the data graph to extract the clustering indicators. We address both of these drawbacks by allowing the data graph itself to be adjusted as part of the clustering procedure. In particular, our Constrained Laplacian Rank (CLR) method learns a graph with exactly k connected components (where k is the number of clusters). We develop two versions of this method, based upon the L1-norm and the L2-norm, which yield two new graph-based clustering objectives. We derive optimization algorithms to solve these objectives. Experimental results on synthetic datasets and real-world benchmark datasets exhibit the effectiveness of this new graph-based clustering method.

Characterizing relationships between people is fundamental for the understanding of narratives. In this work, we address the problem of inferring the polarity of relationships between people in narrative summaries. We formulate the problem as a joint structured prediction for each narrative, and present a general model that combines evidence from linguistic and semantic features, as well as features based on the structure of the social community in the text. We additionally provide a clustering-based approach that can exploit regularities in narrative types. e.g., learn an affinity for love-triangles in romantic stories. On a dataset of movie summaries from Wikipedia, our structured models provide more than 30% error-reduction over a competitive baseline that considers pairs of characters in isolation.

The Augmented Lagragian Method (ALM) and Alternating Direction Method of Multiplier (ADMM) have been powerful optimization methods for general convex programming subject to linear constraint. We consider the convex problem whose objective consists of a smooth part and a nonsmooth but simple part. We propose the Fast Proximal Augmented Lagragian Method (Fast PALM) which achieves the convergence rate O(1/K2), compared with O(1/K) by the traditional PALM. In order to further reduce the per-iteration complexity and handle the multi-blocks problem, we propose the Fast Proximal ADMM with Parallel Splitting (Fast PL-ADMM-PS) method. It also partially improves the rate related to the smooth part of the objective function. Experimental results on both synthesized and real world data demonstrate that our fast methods significantly improve the previous PALM and ADMM