We investigate a class of hierarchical mixtures-of-experts (HME) models where exponential family regression models with generalized linear mean functions of the form psi(ga+fx^Tfgb) are mixed. Here psi(...) is the inverse link function. Suppose the true response y follows an exponential family regression model with mean function belonging to a class of smooth functions of the form psi(h(fx)) where h(...)in W_2^infty (a Sobolev class over [0,1]^{s}). It is shown that the HME probability density functions can approximate the true density, at a rate of O(m^{-2/s}) in L_p norm, and at a rate of O(m^{-4/s}) in Kullback-Leibler divergence. These rates can be achieved within the family of HME structures with no more than s-layers, where s is the dimension of the predictor fx. It is also shown that likelihood-based inference based on HME is consistent in recovering the truth, in the sense that as the sample size n and the number of experts m both increase, the mean square error of the predicted mean response goes to zero. Conditions for such results to hold are stated and discussed.

We describe a method for predicting a classification of an object given classifications of the objects in the training set, assuming that the pairs object/classification are generated by an i.i.d. process from a continuous probability distribution. Our method is a modification of Vapnik's support-vector machine; its main novelty is that it gives not only the prediction itself but also a practicable measure of the evidence found in support of that prediction. We also describe a procedure for assigning degrees of confidence to predictions made by the support vector machine. Some experimental results are presented, and possible extensions of the algorithms are discussed.

Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closely related Dual Coordinate Ascent (DCA) method has been implemented in various software packages, it has so far lacked good convergence analysis. This paper presents a new analysis of Stochastic Dual Coordinate Ascent (SDCA) showing that this class of methods enjoy strong theoretical guarantees that are comparable or better than SGD. This analysis justifies the effectiveness of SDCA for practical applications.

Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks for understanding how dynamical network processes cooperate across widely disparate spatiotemporal scales to solve important computational problems? And second, how can we extract meaningful models of neuronal systems from high dimensional datasets? To aid in these challenges, we give a pedagogical review of a collection of ideas and theoretical methods arising at the intersection of statistical physics, computer science and neurobiology. We introduce the interrelated replica and cavity methods, which originated in statistical physics as powerful ways to quantitatively analyze large highly heterogeneous systems of many interacting degrees of freedom. We also introduce the closely related notion of message passing in graphical models, which originated in computer science as a distributed algorithm capable of solving large inference and optimization problems involving many coupled variables. We then show how both the statistical physics and computer science perspectives can be applied in a wide diversity of contexts to problems arising in theoretical neuroscience and data analysis. Along the way we discuss spin glasses, learning theory, illusions of structure in noise, random matrices, dimensionality reduction, and compressed sensing, all within the unified formalism of the replica method. Moreover, we review recent conceptual connections between message passing in graphical models, and neural computation and learning. Overall, these ideas illustrate how statistical physics and computer science might provide a lens through which we can uncover emergent computational functions buried deep within the dynamical complexities of neuronal networks.

Recently, many regularized procedures have been proposed for variable selection in linear regression, but their performance depends on the tuning parameter selection. Here a criterion for the tuning parameter selection is proposed, which combines the strength of both stability selection and cross-validation and therefore is referred as the prediction and stability selection (PASS). The selection consistency is established assuming the data generating model is a subset of the full model, and the small sample performance is demonstrated through some simulation studies where the assumption is either held or violated.

It is shown that bootstrap approximations of support vector machines (SVMs) based on a general convex and smooth loss function and on a general kernel are consistent. This result is useful to approximate the unknown finite sample distribution of SVMs by the bootstrap approach.

In many classification systems, sensing modalities have different acquisition costs. It is often {\it unnecessary} to use every modality to classify a majority of examples. We study a multi-stage system in a prediction time cost reduction setting, where the full data is available for training, but for a test example, measurements in a new modality can be acquired at each stage for an additional cost. We seek decision rules to reduce the average measurement acquisition cost. We formulate an empirical risk minimization problem (ERM) for a multi-stage reject classifier, wherein the stage $k$ classifier either classifies a sample using only the measurements acquired so far or rejects it to the next stage where more attributes can be acquired for a cost. To solve the ERM problem, we show that the optimal reject classifier at each stage is a combination of two binary classifiers, one biased towards positive examples and the other biased towards negative examples. We use this parameterization to construct stage-by-stage global surrogate risk, develop an iterative algorithm in the boosting framework and present convergence and generalization results. We test our work on synthetic, medical and explosives detection datasets. Our results demonstrate that substantial cost reduction without a significant sacrifice in accuracy is achievable.

Mining discriminative features for graph data has attracted much attention in recent years due to its important role in constructing graph classifiers, generating graph indices, etc. Most measurement of interestingness of discriminative subgraph features are defined on certain graphs, where the structure of graph objects are certain, and the binary edges within each graph represent the "presence" of linkages among the nodes. In many real-world applications, however, the linkage structure of the graphs is inherently uncertain. Therefore, existing measurements of interestingness based upon certain graphs are unable to capture the structural uncertainty in these applications effectively. In this paper, we study the problem of discriminative subgraph feature selection from uncertain graphs. This problem is challenging and different from conventional subgraph mining problems because both the structure of the graph objects and the discrimination score of each subgraph feature are uncertain. To address these challenges, we propose a novel discriminative subgraph feature selection method, DUG, which can find discriminative subgraph features in uncertain graphs based upon different statistical measures including expectation, median, mode and phi-probability. We first compute the probability distribution of the discrimination scores for each subgraph feature based on dynamic programming. Then a branch-and-bound algorithm is proposed to search for discriminative subgraphs efficiently. Extensive experiments on various neuroimaging applications (i.e., Alzheimer's Disease, ADHD and HIV) have been performed to analyze the gain in performance by taking into account structural uncertainties in identifying discriminative subgraph features for graph classification.

Traditional relation extraction predicts relations within some fixed and finite target schema. Machine learning approaches to this task require either manual annotation or, in the case of distant supervision, existing structured sources of the same schema. The need for existing datasets can be avoided by using a universal schema: the union of all involved schemas (surface form predicates as in OpenIE, and relations in the schemas of pre-existing databases). This schema has an almost unlimited set of relations (due to surface forms), and supports integration with existing structured data (through the relation types of existing databases). To populate a database of such schema we present a family of matrix factorization models that predict affinity between database tuples and relations. We show that this achieves substantially higher accuracy than the traditional classification approach. More importantly, by operating simultaneously on relations observed in text and in pre-existing structured DBs such as Freebase, we are able to reason about unstructured and structured data in mutually-supporting ways. By doing so our approach outperforms state-of-the-art distant supervision systems.

In text mining, information retrieval, and machine learning, text documents are commonly represented through variants of sparse Bag of Words (sBoW) vectors (e.g. TF-IDF). Although simple and intuitive, sBoW style representations suffer from their inherent over-sparsity and fail to capture word-level synonymy and polysemy. Especially when labeled data is limited (e.g. in document classification), or the text documents are short (e.g. emails or abstracts), many features are rarely observed within the training corpus. This leads to overfitting and reduced generalization accuracy. In this paper we propose Dense Cohort of Terms (dCoT), an unsupervised algorithm to learn improved sBoW document features. dCoT explicitly models absent words by removing and reconstructing random sub-sets of words in the unlabeled corpus. With this approach, dCoT learns to reconstruct frequent words from co-occurring infrequent words and maps the high dimensional sparse sBoW vectors into a low-dimensional dense representation. We show that the feature removal can be marginalized out and that the reconstruction can be solved for in closed-form. We demonstrate empirically, on several benchmark datasets, that dCoT features significantly improve the classification accuracy across several document classification tasks.