On-line PCA with Optimal Regrets

We carefully investigate the on-line version of PCA, where in each trial a learning algorithm plays a k-dimensional subspace, and suffers the compression loss on the next instance when projected into the chosen subspace. In this setting, we analyze two popular on-line algorithms, Gradient Descent (GD) and Exponentiated Gradient (EG). We show that both algorithms are essentially optimal in the worst-case. This comes as a surprise, since EG is known to perform sub-optimally when the instances are sparse. This different behavior of EG for PCA is mainly related to the non-negativity of the loss in this case, which makes the PCA setting qualitatively different from other settings studied in the literature. Furthermore, we show that when considering regret bounds as function of a loss budget, EG remains optimal and strictly outperforms GD. Next, we study the extension of the PCA setting, in which the Nature is allowed to play with dense instances, which are positive matrices with bounded largest eigenvalue. Again we can show that EG is optimal and strictly better than GD in this setting

Fast Selection of Spectral Variables with B-Spline Compression

The large number of spectral variables in most data sets encountered in spectral chemometrics often renders the prediction of a dependent variable uneasy. The number of variables hopefully can be reduced, by using either projection techniques or selection methods; the latter allow for the interpretation of the selected variables. Since the optimal approach of testing all possible subsets of variables with the prediction model is intractable, an incremental selection approach using a nonparametric statistics is a good option, as it avoids the computationally intensive use of the model itself. It has two drawbacks however: the number of groups of variables to test is still huge, and colinearities can make the results unstable. To overcome these limitations, this paper presents a method to select groups of spectral variables. It consists in a forward-backward procedure applied to the coefficients of a B-Spline representation of the spectra. The criterion used in the forward-backward procedure is the mutual information, allowing to find nonlinear dependencies between variables, on the contrary of the generally used correlation. The spline representation is used to get interpretability of the results, as groups of consecutive spectral variables will be selected. The experiments conducted on NIR spectra from fescue grass and diesel fuels show that the method provides clearly identified groups of selected variables, making interpretation easy, while keeping a low computational load. The prediction performances obtained using the selected coefficients are higher than those obtained by the same method applied directly to the original variables and similar to those obtained using traditional models, although using significantly less spectral variables

Temporal Model Adaptation for Person Re-Identification

Person re-identification is an open and challenging problem in computer vision. Majority of the efforts have been spent either to design the best feature representation or to learn the optimal matching metric. Most approaches have neglected the problem of adapting the selected features or the learned model over time. To address such a problem, we propose a temporal model adaptation scheme with human in the loop. We first introduce a similarity-dissimilarity learning method which can be trained in an incremental fashion by means of a stochastic alternating directions methods of multipliers optimization procedure. Then, to achieve temporal adaptation with limited human effort, we exploit a graph-based approach to present the user only the most informative probe-gallery matches that should be used to update the model. Results on three datasets have shown that our approach performs on par or even better than state-of-the-art approaches while reducing the manual pairwise labeling effort by about 80%

Stochastic Optimization of PCA with Capped MSG

We study PCA as a stochastic optimization problem and propose a novel stochastic approximation algorithm which we refer to as "Matrix Stochastic Gradient" (MSG), as well as a practical variant, Capped MSG. We study the method both theoretically and empirically

Neural networks in geophysical applications

Neural networks are increasingly popular in geophysics. Because they are universal approximators, these tools can approximate any continuous function with an arbitrary precision. Hence, they may yield important contributions to finding solutions to a variety of geophysical applications. However, knowledge of many methods and techniques recently developed to increase the performance and to facilitate the use of neural networks does not seem to be widespread in the geophysical community. Therefore, the power of these tools has not yet been explored to their full extent. In this paper, techniques are described for faster training, better overall performance, i.e., generalization,and the automatic estimation of network size and architecture

Recent Advances in Transfer Learning for Cross-Dataset Visual Recognition: A Problem-Oriented Perspective

This paper takes a problem-oriented perspective and presents a comprehensive review of transfer learning methods, both shallow and deep, for cross-dataset visual recognition. Specifically, it categorises the cross-dataset recognition into seventeen problems based on a set of carefully chosen data and label attributes. Such a problem-oriented taxonomy has allowed us to examine how different transfer learning approaches tackle each problem and how well each problem has been researched to date. The comprehensive problem-oriented review of the advances in transfer learning with respect to the problem has not only revealed the challenges in transfer learning for visual recognition, but also the problems (e.g. eight of the seventeen problems) that have been scarcely studied. This survey not only presents an up-to-date technical review for researchers, but also a systematic approach and a reference for a machine learning practitioner to categorise a real problem and to look up for a possible solution accordingly