We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses the sets to estimate the subspaces. As the geometric structure of the clusters (linear subspaces) forbids proper performance of general distance based approaches such as K-means, many model-specific methods have been proposed. In this paper, we provide new simple and efficient algorithms for this problem. Our statistical analysis shows that the algorithms are guaranteed exact (perfect) clustering performance under certain conditions on the number of points and the affinity be- tween subspaces. These conditions are weaker than those considered in the standard statistical literature. Experimental results on synthetic data generated from the standard unions of subspaces model demonstrate our theory. We also show that our algorithm performs competitively against state-of-the-art algorithms on real-world applications such as motion segmentation and face clustering, with much simpler implementation and lower computational cost.

While topic models can discover patterns of word usage in large corpora, it is difficult to meld this unsupervised structure with noisy, human-provided labels, especially when the label space is large. In this paper, we present a model-Label to Hierarchy (L2H)-that can induce a hierarchy of user-generated labels and the topics associated with those labels from a set of multi-labeled documents. The model is robust enough to account for missing labels from untrained, disparate annotators and provide an interpretable summary of an otherwise unwieldy label set. We show empirically the effectiveness of L2H in predicting held-out words and labels for unseen documents.

At this moment Autonomous cars are probably the biggest and most talked about technology in the Robotics Research Community. In spite of great technological advances over past few years a full edged autonomous car is still far from reality. This article talks about the existing system and discusses the possibility of a Computer Vision enabled driving being superior than the LiDar based system. A detailed overview of privacy violations that might arise from autonomous driving has been discussed in detail both from a technical as well as legal perspective. It has been proved through evidence and arguments that efficient and accurate estimation and efficient solution of the constraint satisfaction problem addressed in the case of autonomous cars are negatively correlated with the preserving the privacy of the user. It is a very difficult trade-off since both are very important aspects and has to be taken into account. The fact that one cannot compromise with the safety issues of the car makes it inevitable to run into serious privacy concerns that might have adverse social and political effects.

Big Data bring new opportunities to modern society and challenges to data scientists. On one hand, Big Data hold great promises for discovering subtle population patterns and heterogeneities that are not possible with small-scale data. On the other hand, the massive sample size and high dimensionality of Big Data introduce unique computational and statistical challenges, including scalability and storage bottleneck, noise accumulation, spurious correlation, incidental endogeneity, and measurement errors. These challenges are distinguished and require new computational and statistical paradigm. This article give overviews on the salient features of Big Data and how these features impact on paradigm change on statistical and computational methods as well as computing architectures. We also provide various new perspectives on the Big Data analysis and computation. In particular, we emphasis on the viability of the sparsest solution in high-confidence set and point out that exogeneous assumptions in most statistical methods for Big Data can not be validated due to incidental endogeneity. They can lead to wrong statistical inferences and consequently wrong scientific conclusions.

This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators' to a distribution over the true error. The variance of this distribution can be interpreted as the (epistemic) uncertainty introduced by the reduced-order model. To model normed errors, the method employs existing rigorous error bounds and residual norms as indicators; numerical experiments show that the method leads to a near-optimal expected effectivity in contrast to typical error bounds. To model errors in general outputs, the method uses dual-weighted residuals---which are amenable to uncertainty control---as indicators. Experiments illustrate that correcting the reduced-order-model output with this surrogate can improve prediction accuracy by an order of magnitude; this contrasts with existing `multifidelity correction' approaches, which often fail for reduced-order models and suffer from the curse of dimensionality. The proposed error surrogates also lead to a notion of `probabilistic rigor', i.e., the surrogate bounds the error with specified probability.

Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on finite sequences cannot capture all of their past dependencies. Spectral arguments show that algorithms which cluster finite-length sequences fail dramatically when the underlying process has long-range temporal correlations and can fail even for processes generated by finite-memory hidden Markov models. We circumvent the curse of dimensionality in rate-distortion analysis of infinite-order processes by casting predictive rate-distortion objective functions in terms of the forward- and reverse-time causal states of computational mechanics. Examples demonstrate that the resulting causal rate-distortion theory substantially improves current predictive rate-distortion analyses.

Artificial Neural Network (ANN) based model is a computational approach commonly used for modeling the complex relationships between input and output parameters. Prediction of the flow rate of a river is a requisite for any successful water resource management and river basin planning. In the current survey, the effectiveness of an Artificial Neural Network was examined to predict the Colorado River discharge. In this modeling process, an ANN model was used to relate the discharge of the Colorado River to such parameters as the amount of precipitation, ambient temperature and snowpack level at a specific time of the year. The model was able to precisely study the impact of climatic parameters on the flow rate of the Colorado River.

Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e.g. for fuel and solar cells, we introduce CombiFD, a framework for factor based pattern decomposition that allows the incorporation of a-priori knowledge as constraints, including complex combinatorial constraints. In addition, we propose a new pattern decomposition algorithm, called AMIQO, based on solving a sequence of (mixed-integer) quadratic programs. Our approach considerably outperforms the state of the art on the materials discovery problem, scaling to larger datasets and recovering more precise and physically meaningful decompositions. We also show the effectiveness of our approach for enforcing background knowledge on other application domains.

We propose a new algorithm called PLUTO for building logistic regression trees to binary response data. PLUTO can capture the nonlinear and interaction patterns in messy data by recursively partitioning the sample space. It fits a simple or a multiple linear logistic regression model in each partition. PLUTO employs the cyclical coordinate descent method for estimation of multiple linear logistic regression models with elastic net penalties, which allows it to deal with high-dimensional data efficiently. The tree structure comprises a graphical description of the data. Together with the logistic regression models, it provides an accurate classifier as well as a piecewise smooth estimate of the probability of "success". PLUTO controls selection bias by: (1) separating split variable selection from split point selection; (2) applying an adjusted chi-squared test to find the split variable instead of exhaustive search. A bootstrap calibration technique is employed to further correct selection bias. Comparison on real datasets shows that on average, the multiple linear PLUTO models predict more accurately than other algorithms.

We explore the idea that authoring a piece of text is an act of maximizing one's expected utility. To make this idea concrete, we consider the societally important decisions of the Supreme Court of the United States. Extensive past work in quantitative political science provides a framework for empirically modeling the decisions of justices and how they relate to text. We incorporate into such a model texts authored by amici curiae ("friends of the court" separate from the litigants) who seek to weigh in on the decision, then explicitly model their goals in a random utility model. We demonstrate the benefits of this approach in improved vote prediction and the ability to perform counterfactual analysis.