Scientists have developed a new artificial intelligence system that can predict court decisions better than legal scholars, even with less information. Researchers, including those from The Stanford Centre for Legal Informatics, used the US Supreme Court Database – which contains information on cases dating back to 1791. Using this, they built an algorithm for predicting any justice's vote at any time. Researchers drew on 16 features of each vote, including the justice, the term, the issue, and the court of origin. They also added other factors, such as whether oral arguments were heard.

One of the most difficult parts of limiting the spread of fake news is that humans have a hard time filtering what is legit from what is bogus. But if humans can't tell the difference between what's real and fake, could machines do any better? In an attempt to answer this question, UC Santa Barbara computer scientist William Wang created LIAR, the largest ever database of fake news in an effort to train machines to automatically detect deception. Comprised of 12,836 examples of statements culled from a decade's worth of short statements from the Pulitzer prize-winning politifact.com, LIAR is an order of magnitude larger than any other fake news database that has been created in response to the 2016 election. To help a machine learning algorithm understand the statements, each of the 12,836 quotes was tagged with information about the truthfulness, subject, context, speaker, state, party, and prior history of inaccurate statements, in addition to a "lengthy analysis report" for the statement.

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Given a collection of data points, non-negative matrix factorization (NMF) suggests to express them as convex combinations of a small set of `archetypes' with non-negative entries. This decomposition is unique only if the true archetypes are non-negative and sufficiently sparse (or the weights are sufficiently sparse), a regime that is captured by the separability condition and its generalizations. In this paper, we study an approach to NMF that can be traced back to the work of Cutler and Breiman (1994) and does not require the data to be separable, while providing a generally unique decomposition. We optimize the trade-off between two objectives: we minimize the distance of the data points from the convex envelope of the archetypes (which can be interpreted as an empirical risk), while minimizing the distance of the archetypes from the convex envelope of the data (which can be interpreted as a data-dependent regularization). The archetypal analysis method of (Cutler, Breiman, 1994) is recovered as the limiting case in which the last term is given infinite weight. We introduce a `uniqueness condition' on the data which is necessary for exactly recovering the archetypes from noiseless data. We prove that, under uniqueness (plus additional regularity conditions on the geometry of the archetypes), our estimator is robust. While our approach requires solving a non-convex optimization problem, we find that standard optimization methods succeed in finding good solutions both for real and synthetic data.

This paper addresses image classification through learning a compact and discriminative dictionary efficiently. Given a structured dictionary with each atom (columns in the dictionary matrix) related to some label, we propose cross-label suppression constraint to enlarge the difference among representations for different classes. Meanwhile, we introduce group regularization to enforce representations to preserve label properties of original samples, meaning the representations for the same class are encouraged to be similar. Upon the cross-label suppression, we don't resort to frequently-used $\ell_0$-norm or $\ell_1$-norm for coding, and obtain computational efficiency without losing the discriminative power for categorization. Moreover, two simple classification schemes are also developed to take full advantage of the learnt dictionary. Extensive experiments on six data sets including face recognition, object categorization, scene classification, texture recognition and sport action categorization are conducted, and the results show that the proposed approach can outperform lots of recently presented dictionary algorithms on both recognition accuracy and computational efficiency.

A function $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is a Sparse Additive Model (SPAM), if it is of the form $f(\mathbf{x}) = \sum_{l \in \mathcal{S}}\phi_{l}(x_l)$ where $\mathcal{S} \subset [d]$, $|\mathcal{S}| \ll d$. Assuming $\phi$'s, $\mathcal{S}$ to be unknown, there exists extensive work for estimating $f$ from its samples. In this work, we consider a generalized version of SPAMs, that also allows for the presence of a sparse number of second order interaction terms. For some $\mathcal{S}_1 \subset [d], \mathcal{S}_2 \subset {[d] \choose 2}$, with $|\mathcal{S}_1| \ll d, |\mathcal{S}_2| \ll d^2$, the function $f$ is now assumed to be of the form: $\sum_{p \in \mathcal{S}_1}\phi_{p} (x_p) + \sum_{(l,l^{\prime}) \in \mathcal{S}_2}\phi_{(l,l^{\prime})} (x_l,x_{l^{\prime}})$. Assuming we have the freedom to query $f$ anywhere in its domain, we derive efficient algorithms that provably recover $\mathcal{S}_1,\mathcal{S}_2$ with finite sample bounds. Our analysis covers the noiseless setting where exact samples of $f$ are obtained, and also extends to the noisy setting where the queries are corrupted with noise. For the noisy setting in particular, we consider two noise models namely: i.i.d Gaussian noise and arbitrary but bounded noise. Our main methods for identification of $\mathcal{S}_2$ essentially rely on estimation of sparse Hessian matrices, for which we provide two novel compressed sensing based schemes. Once $\mathcal{S}_1, \mathcal{S}_2$ are known, we show how the individual components $\phi_p$, $\phi_{(l,l^{\prime})}$ can be estimated via additional queries of $f$, with uniform error bounds. Lastly, we provide simulation results on synthetic data that validate our theoretical findings.

Sparse iterative methods, in particular first-order methods, are known to be among the most effective in solving large-scale two-player zero-sum extensive-form games. The convergence rates of these methods depend heavily on the properties of the distance-generating function that they are based on. We investigate the acceleration of first-order methods for solving extensive-form games through better design of the dilated entropy function---a class of distance-generating functions related to the domains associated with the extensive-form games. By introducing a new weighting scheme for the dilated entropy function, we develop the first distance-generating function for the strategy spaces of sequential games that has no dependence on the branching factor of the player. This result improves the convergence rate of several first-order methods by a factor of $\Omega(b^dd)$, where $b$ is the branching factor of the player, and $d$ is the depth of the game tree. Thus far, counterfactual regret minimization methods have been faster in practice, and more popular, than first-order methods despite their theoretically inferior convergence rates. Using our new weighting scheme and practical tuning we show that, for the first time, the excessive gap technique can be made faster than the fastest counterfactual regret minimization algorithm, CFR+, in practice.

Machine learning has become pervasive in multiple domains, impacting a wide variety of applications, such as knowledge discovery and data mining, natural language processing, information retrieval, computer vision, social and health informatics, ubiquitous computing, etc. Two essential problems of machine learning are how to generate features and how to acquire labels for machines to learn. Particularly, labeling large amount of data for each domain-specific problem can be very time consuming and costly. It has become a key obstacle in making learning protocols realistic in applications. In this paper, we will discuss how to use the existing general-purpose world knowledge to enhance machine learning processes, by enriching the features or reducing the labeling work. We start from the comparison of world knowledge with domain-specific knowledge, and then introduce three key problems in using world knowledge in learning processes, i.e., explicit and implicit feature representation, inference for knowledge linking and disambiguation, and learning with direct or indirect supervision. Finally we discuss the future directions of this research topic.

Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional sparse data, however, the method suffers from slow convergence and high variance due to the heterogeneity in feature sparsity. To mitigate this issue, we introduce a stabilized truncated stochastic gradient descent algorithm. We employ a soft-thresholding scheme on the weight vector where the imposed shrinkage is adaptive to the amount of information available in each feature. The variability in the resulted sparse weight vector is further controlled by stability selection integrated with the informative truncation. To facilitate better convergence, we adopt an annealing strategy on the truncation rate, which leads to a balanced trade-off between exploration and exploitation in learning a sparse weight vector. Numerical experiments show that our algorithm compares favorably with the original algorithm in terms of prediction accuracy, achieved sparsity and stability.

Markov Chain Monte Carlo methods have revolutionised mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of building chains which can explore probability densities efficiently. The method emerges from physics and geometry and these links have been extensively studied by a series of authors through the last thirty years. However, there is currently a gap between the intuitions and knowledge of users of the methodology and our deep understanding of these theoretical foundations. The aim of this review is to provide a comprehensive introduction to the geometric tools used in Hamiltonian Monte Carlo at a level accessible to statisticians, machine learners and other users of the methodology with only a basic understanding of Monte Carlo methods. This will be complemented with some discussion of the most recent advances in the field which we believe will become increasingly relevant to applied scientists.