Feature subset selection arises in many high-dimensional applications of statistics, such as compressed sensing and genomics. The $\ell_0$ penalty is ideal for this task, the caveat being it requires the NP-hard combinatorial evaluation of all models. A recent area of considerable interest is to develop efficient algorithms to fit models with a non-convex $\ell_\gamma$ penalty for $\gamma\in (0,1)$, which results in sparser models than the convex $\ell_1$ or lasso penalty, but is harder to fit. We propose an alternative, termed the horseshoe regularization penalty for feature subset selection, and demonstrate its theoretical and computational advantages. The distinguishing feature from existing non-convex optimization approaches is a full probabilistic representation of the penalty as the negative of the logarithm of a suitable prior, which in turn enables efficient expectation-maximization and local linear approximation algorithms for optimization and MCMC for uncertainty quantification. In synthetic and real data, the resulting algorithms provide better statistical performance, and the computation requires a fraction of time of state-of-the-art non-convex solvers.

The problem of finding overlapping communities in networks has gained much attention recently. Optimization-based approaches use non-negative matrix factorization (NMF) or variants, but the global optimum cannot be provably attained in general. Model-based approaches, such as the popular mixed-membership stochastic blockmodel or MMSB (Airoldi et al., 2008), use parameters for each node to specify the overlapping communities, but standard inference techniques cannot guarantee consistency. We link the two approaches, by (a) establishing sufficient conditions for the symmetric NMF optimization to have a unique solution under MMSB, and (b) proposing a computationally efficient algorithm called GeoNMF that is provably optimal and hence consistent for a broad parameter regime. We demonstrate its accuracy on both simulated and real-world datasets.

Machine learning gets a lot of buzz these days, usually in connection with big data and artificial intelligence (AI). But what exactly is it? Broadly speaking, machine learners are computer algorithms designed for pattern recognition, curve fitting, classification and clustering. The word learning in the term stems from the ability to learn from data. Machine learning is also widely used in data mining and predictive analytics, which some commentators loosely call big data.

This article was written by Natasha Latysheva. Here we publish a short version, with references to full source code in the original article. In machine learning, you may often wish to build predictors that allows to classify things into categories based on some set of associated values. For example, it is possible to provide a diagnosis to a patient based on data from previous patients. Many algorithms have been developed for automated classification, and common ones include random forests, support vector machines, Naïve Bayes classifiers, and many types of neural networks.

Bayesian Statistics continues to remain incomprehensible in the ignited minds of many analysts. Being amazed by the incredible power of machine learning, a lot of us have become unfaithful to statistics. Our focus has narrowed down to exploring machine learning. We fail to understand that machine learning is only one way to solve real world problems. In several situations, it does not help us solve business problems, even though there is data involved in these problems. To say the least, knowledge of statistics will allow you to work on complex analytical problems, irrespective of the size of data. In 1770s, Thomas Bayes introduced'Bayes Theorem'.

This article explains how to run linear regression with R. Check out all this information, here.

When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by the theory? This question is difficult to answer, because in general we do not know how much "predictable variation" there is in the problem. In this paper, we consider approaches motivated by machine learning algorithms as a means of constructing a benchmark for the best attainable level of prediction. We illustrate our methods on the task of predicting human-generated random sequences. Relative to an atheoretical machine learning algorithm benchmark, we find that existing behavioral models explain roughly 15 percent of the predictable variation in this problem. This fraction is robust across several variations on the problem. We also consider a version of this approach for analyzing field data from domains in which human perception and generation of randomness has been used as a conceptual framework; these include sequential decision-making and repeated zero-sum games. In these domains, our framework for testing the completeness of theories provides a way of assessing their effectiveness over different contexts; we find that despite some differences, the existing theories are fairly stable across our field domains in their performance relative to the benchmark. Overall, our results indicate that (i) there is a significant amount of structure in this problem that existing models have yet to capture and (ii) there are rich domains in which machine learning may provide a viable approach to testing completeness.

Domain adaptation algorithms are useful when the distributions of the training and the test data are different. In this paper, we focus on the problem of instrumental variation and time-varying drift in the field of sensors and measurement, which can be viewed as discrete and continuous distributional change in the feature space. We propose maximum independence domain adaptation (MIDA) and semi-supervised MIDA (SMIDA) to address this problem. Domain features are first defined to describe the background information of a sample, such as the device label and acquisition time. Then, MIDA learns a subspace which has maximum independence with the domain features, so as to reduce the inter-domain discrepancy in distributions. A feature augmentation strategy is also designed to project samples according to their backgrounds so as to improve the adaptation. The proposed algorithms are flexible and fast. Their effectiveness is verified by experiments on synthetic datasets and four real-world ones on sensors, measurement, and computer vision. They can greatly enhance the practicability of sensor systems, as well as extend the application scope of existing domain adaptation algorithms by uniformly handling different kinds of distributional change.

Animals (especially humans) have an amazing ability to learn new tasks quickly, and switch between them flexibly. How brains support this ability is largely unknown, both neuroscientifically and algorithmically. One reasonable supposition is that modules drawing on an underlying general-purpose sensory representation are dynamically allocated on a per-task basis. Recent results from neuroscience and artificial intelligence suggest the role of the general purpose visual representation may be played by a deep convolutional neural network, and give some clues how task modules based on such a representation might be discovered and constructed. In this work, we investigate module architectures in an embodied two-dimensional touchscreen environment, in which an agent's learning must occur via interactions with an environment that emits images and rewards, and accepts touches as input. This environment is designed to capture the physical structure of the task environments that are commonly deployed in visual neuroscience and psychophysics. We show that in this context, very simple changes in the nonlinear activations used by such a module can significantly influence how fast it is at learning visual tasks and how suitable it is for switching to new tasks.

An ensemble of models (EM), where each model is constructed on a diverse subset of feature variables, is proposed to rank rare class items ahead of majority class items in a highly unbalanced two class problem. The proposed ensemble relies on an algorithm to group the feature variables into subsets where the variables in a subset work better together in a model and the variables in different subsets work better in separate models. The strength of the EM depends on the algorithm's ability to identify strong and diverse subsets of feature variables. A second phase of ensembling is achieved by aggregating several EMs each optimized on a diverse evaluation metric. The resulting ensemble is called ensemble of models and metrics (EMM). Here, the diverse/complementary evaluation metrics ensure increased diversity among EMs to aggregate. The ensembles are applied to the protein homology data, downloaded from the 2004 KDD cup competition website, to rank proteins in such a way that the rare homologous proteins are found ahead of the majority non-homologous proteins. The ensembles are constructed using feature variables which are various scores from sequence alignments of amino acids in a candidate protein and three dimensional descriptions of a native protein representing functional and structural similarity of proteins. While prediction performances of the EMs are better than the contemporary state-of-the-art ensembles and competitive to the winning procedures of the $2004$ KDD cup competition, the performances of the EMM are found on the top of all. In this application, we have two diverse EMs constructed on two complementary evaluation metrics average precision and rank last, where the former is robust against ranking close homologs and the latter is robust against ranking distant homologs. The advantage of using EMM is that it is robust against both close and distant homologs.