Latent Constrained Correlation Filter.

Correlation filters are special classifiers designed for shift-invariant object recognition, which are robust to pattern distortions. The recent literature shows that combining a set of sub-filters trained based on a single or a small group of images obtains the best performance. The idea is equivalent to estimating variable distribution based on the data sampling (bagging), which can be interpreted as finding solutions (variable distribution approximation) directly from sampled data space. However, this methodology fails to account for the variations existed in the data. In this paper, we introduce an intermediate step-solution sampling-after the data sampling step to form a subspace, in which an optimal solution can be estimated. More specifically, we propose a new method, named latent constrained correlation filters (LCCF), by mapping the correlation filters to a given latent subspace, and develop a new learning framework in the latent subspace that embeds distribution-related constraints into the original problem. To solve the optimization problem, we introduce a subspace-based alternating direction method of multipliers, which is proven to converge at the saddle point. Our approach is successfully applied to three different tasks, including eye localization, car detection, and object tracking. Extensive experiments demonstrate that LCCF outperforms the state-of-the-art methods.11 .

Traveling on discrete embeddings of gene expression.

OBJECTIVE: High-throughput technologies have generated an unprecedented amount of high-dimensional gene expression data. Algorithmic approaches could be extremely useful to distill information and derive compact interpretable representations of the statistical patterns present in the data. This paper proposes a mining approach to extract an informative representation of gene expression profiles based on a generative model called the Counting Grid (CG). METHOD: Using the CG model, gene expression values are arranged on a discrete grid, learned in a way that "similar" co-expression patterns are arranged in close proximity, thus resulting in an intuitive visualization of the dataset. More than this, the model permits to identify the genes that distinguish between classes (e.g. different types of cancer). Finally, each sample can be characterized with a discriminative signature - extracted from the model - that can be effectively employed for classification. RESULTS: A thorough evaluation on several gene expression datasets demonstrate the suitability of the proposed approach from a twofold perspective: numerically, we reached state-of-the-art classification accuracies on 5 datasets out of 7, and similar results when the approach is tested in a gene selection setting (with a stability always above 0.87); clinically, by confirming that many of the genes highlighted by the model as significant play also a key role for cancer biology. CONCLUSION: The proposed framework can be successfully exploited to meaningfully visualize the samples; detect medically relevant genes; properly classify samples.

Capturing Spatial Interdependence in Image Features: The Counting Grid, an Epitomic Representation for Bags of Features.

In recent scene recognition research images or large image regions are often represented as disorganized "bags" of features which can then be analyzed using models originally developed to capture co-variation of word counts in text. However, image feature counts are likely to be constrained in different ways than word counts in text. For example, as a camera pans upwards from a building entrance over its first few floors and then further up into the sky Fig. 1 Fig. 1. Feature counts change slightly as the field of view moves. For example, the abundance of the "car" features is reduced, but the counts of the features found on building facades are increased. The counting grid model accounts for such changes naturally, and it can also account for images of different scenes.

Mapping brains on grids of features for schizophrenia analysis.

This paper exploits the embedding provided by the counting grid model and proposes a framework for the classification and the analysis of brain MRI images. Each brain, encoded by a count of local features, is mapped into a window on a grid of feature distributions. Similar sample are mapped in close proximity on the grid and their commonalities in their feature distributions are reflected in the overlap of windows on the grid. Here we exploited these properties to design a novel kernel and a visualization strategy which we applied to the analysis of schizophrenic patients. Experiments report a clear improvement in classification accuracy as compared with similar methods. Moreover, our visualizations are able to highlight brain clusters and to obtain a visual interpretation of the features related to the disease.

Bags of words models of epitope sets: HIV viral load regression with counting grids.

The immune system gathers evidence of the execution of various molecular processes, both foreign and the cells' own, as time- and space-varying sets of epitopes, small linear or conformational segments of the proteins involved in these processes. Epitopes do not have any obvious ordering in this scheme: The immune system simply sees these epitope sets as disordered "bags" of simple signatures based on whose contents the actions need to be decided. The immense landscape of possible bags of epitopes is shaped by the cellular pathways in various cells, as well as the characteristics of the internal sampling process that chooses and brings epitopes to cellular surface. As a consequence, upon the infection by the same pathogen, different individuals' cells present very different epitope sets. Modeling this landscape should thus be a key step in computational immunology. We show that among possible bag-of-words models, the counting grid is most fit for modeling cellular presentation. We describe each patient by a bag-of-peptides they are likely to present on the cellular surface. In regression tests, we found that compared to the state-of-the-art, counting grids explain more than twice as much of the log viral load variance in these patients. This is potentially a significant advancement in the field, given that a large part of the log viral load variance also depends on the infecting HIV strain, and that HIV polymorphisms themselves are known to strongly associate with HLA types, both effects beyond what is modeled here.

Investigating topic models' capabilities in expression microarray data classification.

In recent years a particular class of probabilistic graphical models-called topic models-has proven to represent an useful and interpretable tool for understanding and mining microarray data. In this context, such models have been almost only applied in the clustering scenario, whereas the classification task has been disregarded by researchers. In this paper, we thoroughly investigate the use of topic models for classification of microarray data, starting from ideas proposed in other fields (e.g., computer vision). A classification scheme is proposed, based on highly interpretable features extracted from topic models, resulting in a hybrid generative-discriminative approach; an extensive experimental evaluation, involving 10 different literature benchmarks, confirms the suitability of the topic models for classifying expression microarray data.

Free Energy Score Spaces: Using Generative Information in Discriminative Classifiers.

A score function induced by a generative model of the data can provide a feature vector of a fixed dimension for each data sample. Data samples themselves may be of differing lengths (e.g., speech segments or other sequential data), but as a score function is based on the properties of the data generation process, it produces a fixed-length vector in a highly informative space, typically referred to as "score space." Discriminative classifiers have been shown to achieve higher performances in appropriately chosen score spaces with respect to what is achievable by either the corresponding generative likelihood-based classifiers or the discriminative classifiers using standard feature extractors. In this paper, we present a novel score space that exploits the free energy associated with a generative model. The resulting free energy score space (FESS) takes into account the latent structure of the data at various levels and can be shown to lead to classification performance that at least matches the performance of the free energy classifier based on the same generative model and the same factorization of the posterior. We also show that in several typical computer vision and computational biology applications the classifiers optimized in FESS outperform the corresponding pure generative approaches, as well as a number of previous approaches combining discriminating and generative models.

Fully non-homogeneous hidden Markov model double net: a generative model for haplotype reconstruction and block discovery.

OBJECTIVE: In the last decade, haplotype reconstruction in unrelated individuals and haplotype block discovery have riveted the attention of computer scientists due to the involved strong computational aspects. Such tasks are usually addressed separately, but recently, statistical techniques have permitted them to be solved jointly. Following this trend we propose a generative model that permits researchers to solve the two problems jointly. METHOD: The model inference is based on variational learning, which permits one to estimate quickly the model parameters while remaining robust even to local minima. The model parameters are then used to segment genotypes into blocks by thresholding a quantitative measure of boundary presence. RESULTS: Experiments on real data are presented, and state-of-the-art systems for haplotype reconstruction and strategies for block estimation are considered as comparison. CONCLUSIONS: The proposed method can be used for a fast and reliable estimation of haplotype frequencies and the relative block structure. Moreover, the method can be easily used as part of a more complex system. The threshold used for block discovery can be related to the quality-of-fit reached in the model learning, resulting in an unsupervised strategy for block estimation.