The Gaussian process latent variable model (GP-LVM) is a popular approach to non-linear probabilistic dimensionality reduction. One design choice for the model is the number of latent variables. We present a spike and slab prior for the GP-LVM and propose an efficient variational inference procedure that gives a lower bound of the log marginal likelihood. The new model provides a more principled approach for selecting latent dimensions than the standard way of thresholding the length-scale parameters. The effectiveness of our approach is demonstrated through experiments on real and simulated data. Further, we extend multi-view Gaussian processes that rely on sharing latent dimensions (known as manifold relevance determination) with spike and slab priors. This allows a more principled approach for selecting a subset of the latent space for each view of data. The extended model outperforms the previous state-of-the-art when applied to a cross-modal multimedia retrieval task.

Improvement guarantees for semi-supervised classifiers can currently only be given under restrictive conditions on the data. We propose a general way to perform semi-supervised parameter estimation for likelihood-based classifiers for which, on the full training set, the estimates are never worse than the supervised solution in terms of the log-likelihood. We argue, moreover, that we may expect these solutions to really improve upon the supervised classifier in particular cases. In a worked-out example for LDA, we take it one step further and essentially prove that its semi-supervised version is strictly better than its supervised counterpart. The two new concepts that form the core of our estimation principle are contrast and pessimism. The former refers to the fact that our objective function takes the supervised estimates into account, enabling the semi-supervised solution to explicitly control the potential improvements over this estimate. The latter refers to the fact that our estimates are conservative and therefore resilient to whatever form the true labeling of the unlabeled data takes on. Experiments demonstrate the improvements in terms of both the log-likelihood and the classification error rate on independent test sets.

We propose a randomized second-order method for optimization known as the Newton Sketch: it is based on performing an approximate Newton step using a randomly projected or sub-sampled Hessian. For self-concordant functions, we prove that the algorithm has super-linear convergence with exponentially high probability, with convergence and complexity guarantees that are independent of condition numbers and related problem-dependent quantities. Given a suitable initialization, similar guarantees also hold for strongly convex and smooth objectives without self-concordance. When implemented using randomized projections based on a sub-sampled Hadamard basis, the algorithm typically has substantially lower complexity than Newton's method. We also describe extensions of our methods to programs involving convex constraints that are equipped with self-concordant barriers. We discuss and illustrate applications to linear programs, quadratic programs with convex constraints, logistic regression and other generalized linear models, as well as semidefinite programs.

In this paper the exact linear relation between the leading eigenvector of the unnormalized modularity matrix and the eigenvectors of the adjacency matrix is developed. Based on this analysis a method to approximate the leading eigenvector of the modularity matrix is given, and the relative error of the approximation is derived. A complete proof of the equivalence between normalized modularity clustering and normalized adjacency clustering is also given. A new metric is defined to describe the agreement of two clustering methods, and some applications and experiments are given to illustrate and corroborate the points that are made in the theoretical development.

In this paper we propose the first non-parametric Bayesian model using Gaussian Processes to make inference on Poisson Point Processes without resorting to gridding the domain or to introducing latent thinning points. Unlike competing models that scale cubically and have a squared memory requirement in the number of data points, our model has a linear complexity and memory requirement. We propose an MCMC sampler and show that our model is faster, more accurate and generates less correlated samples than competing models on both synthetic and real-life data. Finally, we show that our model easily handles data sizes not considered thus far by alternate approaches.

Given a matrix $M$ (not necessarily nonnegative) and a factorization rank $r$, semi-nonnegative matrix factorization (semi-NMF) looks for a matrix $U$ with $r$ columns and a nonnegative matrix $V$ with $r$ rows such that $UV$ is the best possible approximation of $M$ according to some metric. In this paper, we study the properties of semi-NMF from which we develop exact and heuristic algorithms. Our contribution is threefold. First, we prove that the error of a semi-NMF of rank $r$ has to be smaller than the best unconstrained approximation of rank $r-1$. This leads us to a new initialization procedure based on the singular value decomposition (SVD) with a guarantee on the quality of the approximation. Second, we propose an exact algorithm (that is, an algorithm that finds an optimal solution), also based on the SVD, for a certain class of matrices (including nonnegative irreducible matrices) from which we derive an initialization for matrices not belonging to that class. Numerical experiments illustrate that this second approach performs extremely well, and allows us to compute optimal semi-NMF decompositions in many situations. Finally, we analyze the computational complexity of semi-NMF proving its NP-hardness, already in the rank-one case (that is, for $r = 1$), and we show that semi-NMF is sometimes ill-posed (that is, an optimal solution does not exist).

Multiple Additive Regression Trees (MART), an ensemble model of boosted regression trees, is known to deliver high prediction accuracy for diverse tasks, and it is widely used in practice. However, it suffers an issue which we call over-specialization, wherein trees added at later iterations tend to impact the prediction of only a few instances, and make negligible contribution towards the remaining instances. This negatively affects the performance of the model on unseen data, and also makes the model over-sensitive to the contributions of the few, initially added tress. We show that the commonly used tool to address this issue, that of shrinkage, alleviates the problem only to a certain extent and the fundamental issue of over-specialization still remains. In this work, we explore a different approach to address the problem that of employing dropouts, a tool that has been recently proposed in the context of learning deep neural networks. We propose a novel way of employing dropouts in MART, resulting in the DART algorithm. We evaluate DART on ranking, regression and classification tasks, using large scale, publicly available datasets, and show that DART outperforms MART in each of the tasks, with a significant margin. We also show that DART overcomes the issue of over-specialization to a considerable extent.

In contrast, decomposable metrics such as accuracy evaluated on set of examples can be decomposed into a sum of per-example accuracies. Non-decomposability of a performance metric is often desirable as it enables a nonlinear tradeoff between the overall confusion matrix entries: true positives (TP), false positives (FP), true negatives (TN) and false negatives (FN). As a result, non-decomposable performance metrics remain popular for imbalanced and rare event classification in medical diagnosis, fraud detection, information retrieval applications [Lewis and Gale, 1994, Drummond and Holte, 2005, Gu et al., 2009, He and Garcia, 2009], and in other problems where the practitioner is interested in measuring tradeoffs beyond standard classification accuracy. A recent flurry of theoretical results and practical algorithms highlights a growing interest in understanding and optimizing non-decomposable metrics [Dembczynski et al., 2011, Ye et al., 2012, Koyejo et al., 2014, Narasimhan et al., 2014]. Existing theoretical analysis has focused on two distinct approaches for characterizing the population version of the non-decomposable metrics: identified by Ye et al. [2012] as decision theoretic analysis (DTA) and empirical utility maximization (EUM). DTA population utilities measure the expected gain of a classifier on a fixed-size test set, while EUM population utilities are a function 1 of the population confusion matrix. In other words, DTA population utilities measure the the average utility over an infinite set of test sets, each of a fixed size, while EUM population utilities evaluate the performance of a classifier over a single infinitely large test set. It has recently been shown that for EUM based population utilities, the optimal classifier for large classes of non-decomposable binary classification metrics is just the sign of the thresholded conditional probability of the positive class with a metric-dependent threshold [Koyejo et al., 2014, Narasimhan et al., 2014]. In addition, practical algorithms have been proposed for such EUM consistent classification based on direct optimization for the threshold on a held-out validation set.

Person re-identification (re-id), an emerging problem in visual surveillance, deals with maintaining entities of individuals whilst they traverse various locations surveilled by a camera network. From a visual perspective re-id is challenging due to significant changes in visual appearance of individuals in cameras with different pose, illumination and calibration. Globally the challenge arises from the need to maintain structurally consistent matches among all the individual entities across different camera views. We propose PRISM, a structured matching method to jointly account for these challenges. We view the global problem as a weighted graph matching problem and estimate edge weights by learning to predict them based on the co-occurrences of visual patterns in the training examples. These co-occurrence based scores in turn account for appearance changes by inferring likely and unlikely visual co-occurrences appearing in training instances. We implement PRISM on single shot and multi-shot scenarios. PRISM uniformly outperforms state-of-the-art in terms of matching rate while being computationally efficient.

Displaying a document in Middle Eastern languages requires contextual analysis due to different presentational forms for each character of the alphabet. The words of the document will be formed by the joining of the correct positional glyphs representing corresponding presentational forms of the characters. A set of rules defines the joining of the glyphs. As usual, these rules vary from language to language and are subject to interpretation by the software developers. In this paper, we propose a machine learning approach for contextual analysis based on the first order Hidden Markov Model. We will design and build a model for the Farsi language to exhibit this technology. The Farsi model achieves 94 \% accuracy with the training based on a short list of 89 Farsi vocabularies consisting of 2780 Farsi characters. The experiment can be easily extended to many languages including Arabic, Urdu, and Sindhi. Furthermore, the advantage of this approach is that the same software can be used to perform contextual analysis without coding complex rules for each specific language. Of particular interest is that the languages with fewer speakers can have greater representation on the web, since they are typically ignored by software developers due to lack of financial incentives.