Domain adaptation for sequence labeling using hidden Markov models

Most natural language processing systems based on machine learning are not robust to domain shift. For example, a state-of-the-art syntactic dependency parser trained on Wall Street Journal sentences has an absolute drop in performance of more than ten points when tested on textual data from the Web. An efficient solution to make these methods more robust to domain shift is to first learn a word representation using large amounts of unlabeled data from both domains, and then use this representation as features in a supervised learning algorithm. In this paper, we propose to use hidden Markov models to learn word representations for part-of-speech tagging. In particular, we study the influence of using data from the source, the target or both domains to learn the representation and the different ways to represent words using an HMM.Comment: New Directions in Transfer and Multi-Task: Learning Across Domains and Tasks (NIPS Workshop) (2013

Network Flow Algorithms for Structured Sparsity

We consider a class of learning problems that involve a structured sparsity-inducing norm defined as the sum of $\ell_\infty$-norms over groups of variables. Whereas a lot of effort has been put in developing fast optimization methods when the groups are disjoint or embedded in a specific hierarchical structure, we address here the case of general overlapping groups. To this end, we show that the corresponding optimization problem is related to network flow optimization. More precisely, the proximal problem associated with the norm we consider is dual to a quadratic min-cost flow problem. We propose an efficient procedure which computes its solution exactly in polynomial time. Our algorithm scales up to millions of variables, and opens up a whole new range of applications for structured sparse models. We present several experiments on image and video data, demonstrating the applicability and scalability of our approach for various problems.Comment: accepted for publication in Adv. Neural Information Processing Systems, 201

On the Equivalence between Herding and Conditional Gradient Algorithms

We show that the herding procedure of Welling (2009) takes exactly the form of a standard convex optimization algorithm--namely a conditional gradient algorithm minimizing a quadratic moment discrepancy. This link enables us to invoke convergence results from convex optimization and to consider faster alternatives for the task of approximating integrals in a reproducing kernel Hilbert space. We study the behavior of the different variants through numerical simulations. The experiments indicate that while we can improve over herding on the task of approximating integrals, the original herding algorithm tends to approach more often the maximum entropy distribution, shedding more light on the learning bias behind herding

Convex and Network Flow Optimization for Structured Sparsity

We consider a class of learning problems regularized by a structured sparsity-inducing norm defined as the sum of l_2- or l_infinity-norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques when the groups are disjoint or embedded in a hierarchy, we address here the case of general overlapping groups. To this end, we present two different strategies: On the one hand, we show that the proximal operator associated with a sum of l_infinity-norms can be computed exactly in polynomial time by solving a quadratic min-cost flow problem, allowing the use of accelerated proximal gradient methods. On the other hand, we use proximal splitting techniques, and address an equivalent formulation with non-overlapping groups, but in higher dimension and with additional constraints. We propose efficient and scalable algorithms exploiting these two strategies, which are significantly faster than alternative approaches. We illustrate these methods with several problems such as CUR matrix factorization, multi-task learning of tree-structured dictionaries, background subtraction in video sequences, image denoising with wavelets, and topographic dictionary learning of natural image patches.Comment: to appear in the Journal of Machine Learning Research (JMLR

Continuously indexed Potts models on unoriented graphs

International audienceThis paper introduces an extension to undirected graphical models of the classical continuous time Markov chains. This model can be used to solve a transductive or unsupervised multi-class classi- fication problem at each point of a network de- fined as a set of nodes connected by segments of different lengths. The classification is performed not only at the nodes, but at every point of the edge connecting two nodes. This is achieved by constructing a Potts process indexed by the con- tinuum of points forming the edges of the graph. We propose a homogeneous parameterization which satisfies Kolmogorov consistency, and show that classical inference and learning algo- rithms can be applied. We then apply our model to a problem from geo- matics, namely that of labelling city blocks auto- matically with a simple typology of classes (e.g. collective housing) from simple properties of the shape and sizes of buildings of the blocks. Our experiments shows that our model outperform standard MRFs and a discriminative model like logistic regression

Optimization with Sparsity-Inducing Penalties

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate non-smooth norms. The goal of this paper is to present from a general perspective optimization tools and techniques dedicated to such sparsity-inducing penalties. We cover proximal methods, block-coordinate descent, reweighted $\ell_2$-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provide an extensive set of experiments to compare various algorithms from a computational point of view

Convex Relaxation for Combinatorial Penalties

In this paper, we propose an unifying view of several recently proposed structured sparsity-inducing norms. We consider the situation of a model simultaneously (a) penalized by a set- function de ned on the support of the unknown parameter vector which represents prior knowledge on supports, and (b) regularized in Lp-norm. We show that the natural combinatorial optimization problems obtained may be relaxed into convex optimization problems and introduce a notion, the lower combinatorial envelope of a set-function, that characterizes the tightness of our relaxations. We moreover establish links with norms based on latent representations including the latent group Lasso and block-coding, and with norms obtained from submodular functions.Comment: 35 pag

Multi-task feature selection

We address joint feature selection across a group of classification or regression tasks. In many multi-task learning scenarios, different but related tasks share a large proportion of relevant features. We propose a novel type of joint regularization for the parameters of support vector machines in order to couple feature selection across tasks. Intuitively, we extend the ℓ1 regularization for single-task estimation to the multi-task setting. By penalizing the sum of ℓ2-norms of the blocks of coefficients associated with each feature across different tasks, we encourage multiple predictors to have similar parameter sparsity patterns. This approach yields convex, nondifferentiable optimization problems that can be solved efficiently using a simple and scalable extragradient algorithm. We show empirically that our approach outperforms independent ℓ1-based feature selection on several datasets. 1

Consistent probabilistic outputs for protein function prediction

In predicting hierarchical protein function annotations, such as terms in the Gene Ontology (GO), the simplest approach makes predictions for each term independently. However, this approach has the unfortunate consequence that the predictor may assign to a single protein a set of terms that are inconsistent with one another; for example, the predictor may assign a specific GO term to a given protein ('purine nucleotide binding') but not assign the parent term ('nucleotide binding'). Such predictions are difficult to interpret. In this work, we focus on methods for calibrating and combining independent predictions to obtain a set of probabilistic predictions that are consistent with the topology of the ontology. We call this procedure 'reconciliation'. We begin with a baseline method for predicting GO terms from a collection of data types using an ensemble of discriminative classifiers. We apply the method to a previously described benchmark data set, and we demonstrate that the resulting predictions are frequently inconsistent with the topology of the GO. We then consider 11 distinct reconciliation methods: three heuristic methods; four variants of a Bayesian network; an extension of logistic regression to the structured case; and three novel projection methods - isotonic regression and two variants of a Kullback-Leibler projection method. We evaluate each method in three different modes - per term, per protein and joint - corresponding to three types of prediction tasks. Although the principal goal of reconciliation is interpretability, it is important to assess whether interpretability comes at a cost in terms of precision and recall. Indeed, we find that many apparently reasonable reconciliation methods yield reconciled probabilities with significantly lower precision than the original, unreconciled estimates. On the other hand, we find that isotonic regression usually performs better than the underlying, unreconciled method, and almost never performs worse; isotonic regression appears to be able to use the constraints from the GO network to its advantage. An exception to this rule is the high precision regime for joint evaluation, where Kullback-Leibler projection yields the best performance