We present a discriminative nonparametric latent feature relational model (LFRM) for link prediction to automatically infer the dimensionality of latent features. Under the generic RegBayes (regularized Bayesian inference) framework, we handily incorporate the prediction loss with probabilistic inference of a Bayesian model; set distinct regularization parameters for different types of links to handle the imbalance issue in real networks; and unify the analysis of both the smooth logistic log-loss and the piecewise linear hinge loss. For the nonconjugate posterior inference, we present a simple Gibbs sampler via data augmentation, without making restricting assumptions as done in variational methods. We further develop an approximate sampler using stochastic gradient Langevin dynamics to handle large networks with hundreds of thousands of entities and millions of links, orders of magnitude larger than what existing LFRM models can process. Extensive studies on various real networks show promising performance.

Understanding a user's motivations provides valuable information beyond the ability to recommend items. Quite often this can be accomplished by perusing both ratings and review texts, since it is the latter where the reasoning for specific preferences is explicitly expressed. Unfortunately matrix factorization approaches to recommendation result in large, complex models that are difficult to interpret and give recommendations that are hard to clearly explain to users. In contrast, in this paper, we attack this problem through succinct additive co-clustering. We devise a novel Bayesian technique for summing co-clusterings of Poisson distributions. With this novel technique we propose a new Bayesian model for joint collaborative filtering of ratings and text reviews through a sum of simple co-clusterings. The simple structure of our model yields easily interpretable recommendations. Even with a simple, succinct structure, our model outperforms competitors in terms of predicting ratings with reviews.

Shrinkage algorithms are of great importance in almost every area of statistics due to the increasing impact of big data. Especially time series analysis benefits from efficient and rapid estimation techniques such as the lasso. However, currently lasso type estimators for autoregressive time series models still focus on models with homoscedastic residuals. Therefore, an iteratively reweighted adaptive lasso algorithm for the estimation of time series models under conditional heteroscedasticity is presented in a high-dimensional setting. The asymptotic behaviour of the resulting estimator is analysed. It is found that the proposed estimation procedure performs substantially better than its homoscedastic counterpart. A special case of the algorithm is suitable to compute the estimated multivariate AR-ARCH type models efficiently. Extensions to the model like periodic AR-ARCH, threshold AR-ARCH or ARMA-GARCH are discussed. Finally, different simulation results and applications to electricity market data and returns of metal prices are shown.

Latent variable models are a fundamental modeling tool in machine learning applications, but they present significant computational and analytical challenges. The popular EM algorithm and its variants, is a much used algorithmic tool; yet our rigorous understanding of its performance is highly incomplete. Recently, work in Balakrishnan et al. (2014) has demonstrated that for an important class of problems, EM exhibits linear local convergence. In the high-dimensional setting, however, the M-step may not be well defined. We address precisely this setting through a unified treatment using regularization. While regularization for high-dimensional problems is by now well understood, the iterative EM algorithm requires a careful balancing of making progress towards the solution while identifying the right structure (e.g., sparsity or low-rank). In particular, regularizing the M-step using the state-of-the-art high-dimensional prescriptions (e.g., Wainwright (2014)) is not guaranteed to provide this balance. Our algorithm and analysis are linked in a way that reveals the balance between optimization and statistical errors. We specialize our general framework to sparse gaussian mixture models, high-dimensional mixed regression, and regression with missing variables, obtaining statistical guarantees for each of these examples.

We introduce single-set spectral sparsification as a deterministic sampling based feature selection technique for regularized least squares classification, which is the classification analogue to ridge regression. The method is unsupervised and gives worst-case guarantees of the generalization power of the classification function after feature selection with respect to the classification function obtained using all features. We also introduce leverage-score sampling as an unsupervised randomized feature selection method for ridge regression. We provide risk bounds for both single-set spectral sparsification and leverage-score sampling on ridge regression in the fixed design setting and show that the risk in the sampled space is comparable to the risk in the full-feature space. We perform experiments on synthetic and real-world datasets, namely a subset of TechTC-300 datasets, to support our theory. Experimental results indicate that the proposed methods perform better than the existing feature selection methods.

We develop necessary and sufficient conditions and a novel provably consistent and efficient algorithm for discovering topics (latent factors) from observations (documents) that are realized from a probabilistic mixture of shared latent factors that have certain properties. Our focus is on the class of topic models in which each shared latent factor contains a novel word that is unique to that factor, a property that has come to be known as separability. Our algorithm is based on the key insight that the novel words correspond to the extreme points of the convex hull formed by the row-vectors of a suitably normalized word co-occurrence matrix. We leverage this geometric insight to establish polynomial computation and sample complexity bounds based on a few isotropic random projections of the rows of the normalized word co-occurrence matrix. Our proposed random-projections-based algorithm is naturally amenable to an efficient distributed implementation and is attractive for modern web-scale distributed data mining applications.

A method for large scale Gaussian process classification has been recently proposed based on expectation propagation (EP). Such a method allows Gaussian process classifiers to be trained on very large datasets that were out of the reach of previous deployments of EP and has been shown to be competitive with related techniques based on stochastic variational inference. Nevertheless, the memory resources required scale linearly with the dataset size, unlike in variational methods. This is a severe limitation when the number of instances is very large. Here we show that this problem is avoided when stochastic EP is used to train the model.

We analyze in this paper a random feature map based on a theory of invariance I-theory introduced recently. More specifically, a group invariant signal signature is obtained through cumulative distributions of group transformed random projections. Our analysis bridges invariant feature learning with kernel methods, as we show that this feature map defines an expected Haar integration kernel that is invariant to the specified group action. We show how this non-linear random feature map approximates this group invariant kernel uniformly on a set of $N$ points. Moreover, we show that it defines a function space that is dense in the equivalent Invariant Reproducing Kernel Hilbert Space. Finally, we quantify error rates of the convergence of the empirical risk minimization, as well as the reduction in the sample complexity of a learning algorithm using such an invariant representation for signal classification, in a classical supervised learning setting.

Adjusted for chance measures are widely used to compare partitions/clusterings of the same data set. In particular, the Adjusted Rand Index (ARI) based on pair-counting, and the Adjusted Mutual Information (AMI) based on Shannon information theory are very popular in the clustering community. Nonetheless it is an open problem as to what are the best application scenarios for each measure and guidelines in the literature for their usage are sparse, with the result that users often resort to using both. Generalized Information Theoretic (IT) measures based on the Tsallis entropy have been shown to link pair-counting and Shannon IT measures. In this paper, we aim to bridge the gap between adjustment of measures based on pair-counting and measures based on information theory. We solve the key technical challenge of analytically computing the expected value and variance of generalized IT measures. This allows us to propose adjustments of generalized IT measures, which reduce to well known adjusted clustering comparison measures as special cases. Using the theory of generalized IT measures, we are able to propose the following guidelines for using ARI and AMI as external validation indices: ARI should be used when the reference clustering has large equal sized clusters; AMI should be used when the reference clustering is unbalanced and there exist small clusters.

Multi-instance learning (MIL) has a wide range of applications due to its distinctive characteristics. Although many state-of-the-art algorithms have achieved decent performances, a plurality of existing methods solve the problem only in instance level rather than excavating relations among bags. In this paper, we propose an efficient algorithm to describe each bag by a corresponding feature vector via comparing it with other bags. In other words, the crucial information of a bag is extracted from the similarity between that bag and other reference bags. In addition, we apply extensions of Hausdorff distance to representing the similarity, to a certain extent, overcoming the key challenge of MIL problem, the ambiguity of instances' labels in positive bags. Experimental results on benchmarks and text categorization tasks show that the proposed method outperforms the previous state-of-the-art by a large margin.