In this work, we first show that feature selection methods other than boosting can also be used for training an efficient object detector. In particular, we introduce Greedy Sparse Linear Discriminant Analysis (GSLDA) \cite{Moghaddam2007Fast} for its conceptual simplicity and computational efficiency; and slightly better detection performance is achieved compared with \cite{Viola2004Robust}. Moreover, we propose a new technique, termed Boosted Greedy Sparse Linear Discriminant Analysis (BGSLDA), to efficiently train a detection cascade. BGSLDA exploits the sample re-weighting property of boosting and the class-separability criterion of GSLDA.

We show that the two-stage adaptive Lasso procedure (Zou, 2006) is consistent for high-dimensional model selection in linear and Gaussian graphical models. Our conditions for consistency cover more general situations than those accomplished in previous work: we prove that restricted eigenvalue conditions (Bickel et al., 2008) are also sufficient for sparse structure estimation.

We study the problem of estimating multiple linear regression equations for the purpose of both prediction and variable selection. Following recent work on multi-task learning Argyriou et al. [2008], we assume that the regression vectors share the same sparsity pattern. This means that the set of relevant predictor variables is the same across the different equations. This assumption leads us to consider the Group Lasso as a candidate estimation method. We show that this estimator enjoys nice sparsity oracle inequalities and variable selection properties. The results hold under a certain restricted eigenvalue condition and a coherence condition on the design matrix, which naturally extend recent work in Bickel et al. [2007], Lounici [2008]. In particular, in the multi-task learning scenario, in which the number of tasks can grow, we are able to remove completely the effect of the number of predictor variables in the bounds. Finally, we show how our results can be extended to more general noise distributions, of which we only require the variance to be finite.

1-Nearest Neighbor with the Dynamic Time Warping (DTW) distance is one of the most effective classifiers on time series domain. Since the global constraint has been introduced in speech community, many global constraint models have been proposed including Sakoe-Chiba (S-C) band, Itakura Parallelogram, and Ratanamahatana-Keogh (R-K) band. The R-K band is a general global constraint model that can represent any global constraints with arbitrary shape and size effectively. However, we need a good learning algorithm to discover the most suitable set of R-K bands, and the current R-K band learning algorithm still suffers from an 'overfitting' phenomenon. In this paper, we propose two new learning algorithms, i.e., band boundary extraction algorithm and iterative learning algorithm. The band boundary extraction is calculated from the bound of all possible warping paths in each class, and the iterative learning is adjusted from the original R-K band learning. We also use a Silhouette index, a well-known clustering validation technique, as a heuristic function, and the lower bound function, LB_Keogh, to enhance the prediction speed. Twenty datasets, from the Workshop and Challenge on Time Series Classification, held in conjunction of the SIGKDD 2007, are used to evaluate our approach.

For tensor decompositions such as HOSVD and ParaFac, the objective functions are nonconvex. This implies, theoretically, there exists a large number of local optimas: starting from different starting point, the iteratively improved solution will converge to different local solutions. This non-uniqueness present a stability and reliability problem for image compression and retrieval. In this paper, we present the results of a comprehensive investigation of this problem. We found that although all tensor decomposition algorithms fail to reach a unique global solution on random data and severely scrambled data; surprisingly however, on all real life several data sets (even with substantial scramble and occlusions), HOSVD always produce the unique global solution in the parameter region suitable to practical applications, while ParaFac produce non-unique solutions. We provide an eigenvalue based rule for the assessing the solution uniqueness.

This paper addresses the general problem of domain adaptation which arises in a variety of applications where the distribution of the labeled sample available somewhat differs from that of the test data. Building on previous work by Ben-David et al. (2007), we introduce a novel distance between distributions, discrepancy distance, that is tailored to adaptation problems with arbitrary loss functions. We give Rademacher complexity bounds for estimating the discrepancy distance from finite samples for different loss functions. Using this distance, we derive novel generalization bounds for domain adaptation for a wide family of loss functions. We also present a series of novel adaptation bounds for large classes of regularization-based algorithms, including support vector machines and kernel ridge regression based on the empirical discrepancy. This motivates our analysis of the problem of minimizing the empirical discrepancy for various loss functions for which we also give novel algorithms. We report the results of preliminary experiments that demonstrate the benefits of our discrepancy minimization algorithms for domain adaptation.

The runtime for Kernel Partial Least Squares (KPLS) to compute the fit is quadratic in the number of examples. However, the necessity of obtaining sensitivity measures as degrees of freedom for model selection or confidence intervals for more detailed analysis requires cubic runtime, and thus constitutes a computational bottleneck in real-world data analysis. We propose a novel algorithm for KPLS which not only computes (a) the fit, but also (b) its approximate degrees of freedom and (c) error bars in quadratic runtime. The algorithm exploits a close connection between Kernel PLS and the Lanczos algorithm for approximating the eigenvalues of symmetric matrices, and uses this approximation to compute the trace of powers of the kernel matrix in quadratic runtime.

Conformal predictors, introduced by Vovk et al. (2005), serve to build prediction intervals by exploiting a notion of conformity of the new data point with previously observed data. In the present paper, we propose a novel method for constructing prediction intervals for the response variable in multivariate linear models. The main emphasis is on sparse linear models, where only few of the covariates have significant influence on the response variable even if their number is very large. Our approach is based on combining the principle of conformal prediction with the $\ell_1$ penalized least squares estimator (LASSO). The resulting confidence set depends on a parameter $\epsilon>0$ and has a coverage probability larger than or equal to $1-\epsilon$. The numerical experiments reported in the paper show that the length of the confidence set is small. Furthermore, as a by-product of the proposed approach, we provide a data-driven procedure for choosing the LASSO penalty. The selection power of the method is illustrated on simulated data.

In this paper we propose a computationally efficient algorithm for on-line variable selection in multivariate regression problems involving high dimensional data streams. The algorithm recursively extracts all the latent factors of a partial least squares solution and selects the most important variables for each factor. This is achieved by means of only one sparse singular value decomposition which can be efficiently updated on-line and in an adaptive fashion. Simulation results based on artificial data streams demonstrate that the algorithm is able to select important variables in dynamic settings where the correlation structure among the observed streams is governed by a few hidden components and the importance of each variable changes over time. We also report on an application of our algorithm to a multivariate version of the "enhanced index tracking" problem using financial data streams. The application consists of performing on-line asset allocation with the objective of overperforming two benchmark indices simultaneously.

A new method is presented, that can help a person become aware of his or her unconscious preferences, and convey them to others in the form of verbal explanation. The method combines the concepts of reflection, visualization, and verbalization. The method was tested in an experiment where the unconscious preferences of the subjects for various artworks were investigated. In the experiment, two lessons were learned. The first is that it helps the subjects become aware of their unconscious preferences to verbalize weak preferences as compared with strong preferences through discussion over preference diagrams. The second is that it is effective to introduce an adjustable factor into visualization to adapt to the differences in the subjects and to foster their mutual understanding.