In order to investigate the breast cancer prediction problem on the aging population with the grades of DCIS, we conduct a tree augmented naive Bayesian network experiment trained and tested on a large clinical dataset including consecutive diagnostic mammography examinations, consequent biopsy outcomes and related cancer registry records in the population of women across all ages. Our tasks are to classify the conventional "Benign vs. Malignant" and the new "Benign/LG vs. IntG/HG/Invasive" based on mammography examination features and patient demographic information, specifically to predict the probability of malignancy, for the biopsy threshold setting and the biopsy decision making. The aggregated results of our tenfold cross validation method recommend a biopsy threshold higher than 2% for the aging population. The Receiver Operating Characteristic curves and the Precision-Recall curves by aggregating the tenfold cross validation results are interesting.

We present a novel hybrid algorithm for Bayesian network structure learning, called H2PC. It first reconstructs the skeleton of a Bayesian network and then performs a Bayesian-scoring greedy hill-climbing search to orient the edges. The algorithm is based on divide-and-conquer constraint-based subroutines to learn the local structure around a target variable. We conduct two series of experimental comparisons of H2PC against Max-Min Hill-Climbing (MMHC), which is currently the most powerful state-of-the-art algorithm for Bayesian network structure learning. First, we use eight well-known Bayesian network benchmarks with various data sizes to assess the quality of the learned structure returned by the algorithms. Our extensive experiments show that H2PC outperforms MMHC in terms of goodness of fit to new data and quality of the network structure with respect to the true dependence structure of the data. Second, we investigate H2PC's ability to solve the multi-label learning problem. We provide theoretical results to characterize and identify graphically the so-called minimal label powersets that appear as irreducible factors in the joint distribution under the faithfulness condition. The multi-label learning problem is then decomposed into a series of multi-class classification problems, where each multi-class variable encodes a label powerset. H2PC is shown to compare favorably to MMHC in terms of global classification accuracy over ten multi-label data sets covering different application domains. Overall, our experiments support the conclusions that local structural learning with H2PC in the form of local neighborhood induction is a theoretically well-motivated and empirically effective learning framework that is well suited to multi-label learning. The source code (in R) of H2PC as well as all data sets used for the empirical tests are publicly available.

We introduce a variant of (sparse) PCA in which the set of feasible support sets is determined by a graph. In particular, we consider the following setting: given a directed acyclic graph $G$ on $p$ vertices corresponding to variables, the non-zero entries of the extracted principal component must coincide with vertices lying along a path in $G$. From a statistical perspective, information on the underlying network may potentially reduce the number of observations required to recover the population principal component. We consider the canonical estimator which optimally exploits the prior knowledge by solving a non-convex quadratic maximization on the empirical covariance. We introduce a simple network and analyze the estimator under the spiked covariance model. We show that side information potentially improves the statistical complexity. We propose two algorithms to approximate the solution of the constrained quadratic maximization, and recover a component with the desired properties. We empirically evaluate our schemes on synthetic and real datasets.

We develop a worst-case analysis of aggregation of classifier ensembles for binary classification. The task of predicting to minimize error is formulated as a game played over a given set of unlabeled data (a transductive setting), where prior label information is encoded as constraints on the game. The minimax solution of this game identifies cases where a weighted combination of the classifiers can perform significantly better than any single classifier.

Deep neural networks (DNNs) and other types of deep learning architecture have made significant advances [3, 4]. In both well-benchmarked tasks and real-world applications, such as automatic speech recognition [21, 34, 44] and image recognition [29, 48], deep learning architectures have achieved an unprecedented level of success and have generated major impact. Arguably, the most instrumental factors contributing to their success are: (1) learning from a huge amount of training data for highly complex models with millions to billions of parameters; (2) adopting simple but effective optimization methods such as stochastic gradient descent; (3) combatting overfitting with new schemes such as dropout [23]; and (4) computing with massive parallelism on GPUs. New techniques as well as "tricks of the trade" are frequently invented and added to the toolboxes for machine learning researchers and practitioners. In stark contrast, there have been many fewer publicly known successful applications of kernel methods (such as support vector machines) to problems at a scale comparable to the speech and image recognition problems tackled by DNNs. This is a surprising chasm, noting that kernel methods have been extensively studied both theoretically and empirically for their power of modeling highly nonlinear data [43]. Moreover, the connection between kernel methods and (infinite) neural networks has also been long noted [35, 51, 11]. Nonetheless, a common misconception is that it may be difficult, if not impossible, for kernel methods to catch up with deep learning methods in addressing large-scale learning problems.

Learning the network structure underlying data is an important problem in machine learning. This paper introduces a novel prior to study the inference of scale-free networks, which are widely used to model social and biological networks. The prior not only favors a desirable global node degree distribution, but also takes into consideration the relative strength of all the possible edges adjacent to the same node and the estimated degree of each individual node. To fulfill this, ranking is incorporated into the prior, which makes the problem challenging to solve. We employ an ADMM (alternating direction method of multipliers) framework to solve the Gaussian Graphical model regularized by this prior. Our experiments on both synthetic and real data show that our prior not only yields a scale-free network, but also produces many more correctly predicted edges than the others such as the scale-free inducing prior, the hub-inducing prior and the $l_1$ norm.

This paper considers the problem of estimating multiple related Gaussian graphical models from a $p$-dimensional dataset consisting of different classes. Our work is based upon the formulation of this problem as group graphical lasso. This paper proposes a novel hybrid covariance thresholding algorithm that can effectively identify zero entries in the precision matrices and split a large joint graphical lasso problem into small subproblems. Our hybrid covariance thresholding method is superior to existing uniform thresholding methods in that our method can split the precision matrix of each individual class using different partition schemes and thus split group graphical lasso into much smaller subproblems, each of which can be solved very fast. In addition, this paper establishes necessary and sufficient conditions for our hybrid covariance thresholding algorithm. The superior performance of our thresholding method is thoroughly analyzed and illustrated by a few experiments on simulated data and real gene expression data.

With few exceptions, the field of Machine Learning (ML) research has largely ignored the browser as a computational engine. Beyond an educational resource for ML, the browser has vast potential to not only improve the state-of-the-art in ML research, but also, inexpensively and on a massive scale, to bring sophisticated ML learning and prediction to the public at large. This paper introduces MLitB, a prototype ML framework written entirely in JavaScript, capable of performing large-scale distributed computing with heterogeneous classes of devices. The development of MLitB has been driven by several underlying objectives whose aim is to make ML learning and usage ubiquitous (by using ubiquitous compute devices), cheap and effortlessly distributed, and collaborative. This is achieved by allowing every internet capable device to run training algorithms and predictive models with no software installation and by saving models in universally readable formats. Our prototype library is capable of training deep neural networks with synchronized, distributed stochastic gradient descent. MLitB offers several important opportunities for novel ML research, including: development of distributed learning algorithms, advancement of web GPU algorithms, novel field and mobile applications, privacy preserving computing, and green grid-computing. MLitB is available as open source software.

In this paper we propose a model that combines the strengths of RNNs and SGVB: the Variational Recurrent Auto-Encoder (VRAE). Such a model can be used for efficient, large scale unsupervised learning on time series data, mapping the time series data to a latent vector representation. The model is generative, such that data can be generated from samples of the latent space. An important contribution of this work is that the model can make use of unlabeled data in order to facilitate supervised training of RNNs by initialising the weights and network state.

It is well-known that learning predictive models capable of dealing with outputs that are richer than binary outputs (e.g., multiclass or multilabel) and for which theoretical guarantees exist is still a realm of intensive investigations. From a practical standpoint, a lot of relaxations for learning with complex outputs have been devised. A common approach consists in decomposing the output space into "simpler" spaces so that the learning problem at hand can be reduced to a few easier (i.e., binary) learning tasks. For instance, this is the idea spurred by the Error-Correcting Output Codes (Dietterich & Bakiri, 1995) that makes possible to reduce multiclass or multilabel problems into binary classification tasks,e.g., (Allwein et al., 2001; Mroueh et al., 2012; Read et al., 2011; Tsoumakas & Vlahavas, 2007; Zhang & Schneider, 2012). In our work, we study the problem of complex output prediction by focusing on prediction functions that take the form of a weighted majority vote over a set of complex output classifiers (or voters). Recall that ensemble methods can all be seen as majority vote learning procedures (Dietterich, 2000; Re & Valentini, 2012). Methods such as Bagging (Breiman, 1996), Boosting (Schapire & Singer, 1999) and Random Forests (Breiman, 2001) are representative voting methods. Cortes et al. (2014) have proposed various ensemble methods for the structured output prediction framework. Note also that majority votes are also central to the Bayesian approach (Gelman et al., 2004) with the notion of Bayesian model averaging (Domingos, 2000; Haussler et al., 1994) and most of kernel-based predictors, such as the Support Vector Machines (Boser et al., 1992; Cortes & Vapnik, 1995) may be viewed as weighted majority votes as well: for binary classification, where the predicted class for some input x is computed as the sign of