Importance weighting is a fundamental procedure in statistics and machine learning that weights the objective function or probability distribution based on the importance of the instance in some sense. The simplicity and usefulness of the idea has led to many applications of importance weighting. For example, it is known that supervised learning under an assumption about the difference between the training and test distributions, called distribution shift, can guarantee statistically desirable properties through importance weighting by their density ratio. This survey summarizes the broad applications of importance weighting in machine learning and related research.

Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be computationally much more expensive. In this paper, we demonstrate the surprising fact that sparse PCA can be easier than PCA in practice, and that it can be reliably applied to very large data sets. This comes from a rigorous feature elimination pre-processing result, coupled with the favorable fact that features in real-life data typically have exponentially decreasing variances, which allows for many features to be eliminated. We introduce a fast block coordinate ascent algorithm with much better computational complexity than the existing first-order ones. We provide experimental results obtained on text corpora involving millions of documents and hundreds of thousands of features. These results illustrate how Sparse PCA can help organize a large corpus of text data in a user-interpretable way, providing an attractive alternative approach to topic models.

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A multilinear subspace regression model based on so called latent variable decomposition is introduced. Unlike standard regression methods which typically employ matrix (2D) data representations followed by vector subspace transformations, the proposed approach uses tensor subspace transformations to model common latent variables across both the independent and dependent data. The proposed approach aims to maximize the correlation between the so derived latent variables and is shown to be suitable for the prediction of multidimensional dependent data from multidimensional independent data, where for the estimation of the latent variables we introduce an algorithm based on Multilinear Singular Value Decomposition (MSVD) on a specially defined cross-covariance tensor. It is next shown that in this way we are also able to unify the existing Partial Least Squares (PLS) and N-way PLS regression algorithms within the same framework. Simulations on benchmark synthetic data confirm the advantages of the proposed approach, in terms of its predictive ability and robustness, especially for small sample sizes. The potential of the proposed technique is further illustrated on a real world task of the decoding of human intracranial electrocorticogram (ECoG) from a simultaneously recorded scalp electroencephalograph (EEG).

Warped Gaussian processes (WGP) [1] model output observations in regression tasks as a parametric nonlinear transformation of a Gaussian process (GP). The use of this nonlinear transformation, which is included as part of the probabilistic model, was shown to enhance performance by providing a better prior model on several data sets. In order to learn its parameters, maximum likelihood was used. In this work we show that it is possible to use a non-parametric nonlinear transformation in WGP and variationally integrate it out. The resulting Bayesian WGP is then able to work in scenarios in which the maximum likelihood WGP failed: Low data regime, data with censored values, classification, etc. We demonstrate the superior performance of Bayesian warped GPs on several real data sets.

In the conventional approaches for supervised parametric learning, relations between data and target variables are provided through training sets consisting of pairs of corresponded data and target variables. In this work, we describe a new learning scheme for parametric learning, in which the target variables y can be modeled with a prior model p(y) and the relations between data and target variables are estimated with p(y) and a set of uncorresponded data X in training.

Probabilistic approaches to computer vision typically assume a centralized setting, with the algorithm granted access to all observed data points. However, many problems in wide-area surveillance can benefit from distributed modeling, either because of physical or computational constraints. Most distributed models to date use algebraic approaches (such as distributed SVD) and as a result cannot explicitly deal with missing data. In this work we present an approach to estimation and learning of generative probabilistic models in a distributed context where certain sensor data can be missing. In particular, we show how traditional centralized models, such as probabilistic PCA and missing-data PPCA, can be learned when the data is distributed across a network of sensors. We demonstrate the utility of this approach on the problem of distributed affine structure from motion. Our experiments suggest that the accuracy of the learned probabilistic structure and motion models rivals that of traditional centralized factorization methods while being able to handle challenging situations such as missing or noisy observations.

In the superset label learning problem (SLL), each training instance provides a set of candidate labels of which one is the true label of the instance. As in ordinary regression, the candidate label set is a noisy version of the true label. In this work, we solve the problem by maximizing the likelihood of the candidate label sets of training instances. We propose a probabilistic model, the Logistic Stick-Breaking Conditional Multinomial Model (LSB-CMM), to do the job. The LSB-CMM is derived from the logistic stick-breaking process. It first maps data points to mixture components and then assigns to each mixture component a label drawn from a component-specific multinomial distribution.

Learning the number of clusters is a key problem in data clustering. We present dip-means, a novel robust incremental method to learn the number of data clusters that can be used as a wrapper around any iterative clustering algorithm of k-means family. In contrast to many popular methods which make assumptions about the underlying cluster distributions, dip-means only assumes a fundamental cluster property: each cluster to admit a unimodal distribution. The proposed algorithm considers each cluster member as an individual'viewer' and applies a univariate statistic hypothesis test for unimodality (dip-test) on the distribution of distances between the viewer and the cluster members. Important advantages are: i) the unimodality test is applied on univariate distance vectors, ii) it can be directly applied with kernel-based methods, since only the pairwise distances are involved in the computations. Experimental results on artificial and real datasets indicate the effectiveness of our method and its superiority over analogous approaches.

We develop a novel approach for supervised learning based on adaptively partitioning the feature space into different regions and learning local region-specific classifiers. We formulate an empirical risk minimization problem that incorporates both partitioning and classification in to a single global objective. We show that space partitioning can be equivalently reformulated as a supervised learning problem and consequently any discriminative learning method can be utilized in conjunction with our approach. Nevertheless, we consider locally linear schemes by learning linear partitions and linear region classifiers. Locally linear schemes can not only approximate complex decision boundaries and ensure low training error but also provide tight control on over-fitting and generalization error. We train locally linear classifiers by using LDA, logistic regression and perceptrons, and so our scheme is scalable to large data sizes and high-dimensions. We present experimental results demonstrating improved performance over state of the art classification techniques on benchmark datasets. We also show improved robustness to label noise.