Data lying in a high-dimensional ambient space are commonly thought to have a much lower intrinsic dimension. In particular, the data may be concentrated near a lower-dimensional subspace or manifold. There is an immense literature focused on approximating the unknown subspace, and in exploiting such approximations in clustering, data compression, and building of predictive models. Most of the literature relies on approximating subspaces using a locally linear, and potentially multiscale, dictionary. In this article, we propose a simple and general alternative, which instead uses pieces of spheres, or spherelets, to locally approximate the unknown subspace. Building on this idea, we develop a simple and computationally efficient algorithm for subspace learning and clustering. Results relative to state-of-the-art competitors show dramatic gains in ability to accurately approximate the subspace with orders of magnitude fewer components. This leads to substantial gains in data compressibility, few clusters and hence better interpretability, and much lower MSE based on small to moderate sample sizes. Basic theory on approximation accuracy is presented, and the methods are applied to multiple examples.

This paper introduces the YouTube-8M Video Understanding Challenge hosted as a Kaggle competition and also describes my approach to experimenting with various models. For each of my experiments, I provide the score result as well as possible improvements to be made. Towards the end of the paper, I discuss the various ensemble learning techniques that I applied on the dataset which significantly boosted my overall competition score. At last, I discuss the exciting future of video understanding research and also the many applications that such research could significantly improve.

We are increasingly surrounded by artificially intelligent technology that takes decisions and executes actions on our behalf. This creates a pressing need for general means to communicate with, instruct and guide artificial agents, with human language the most compelling means for such communication. To achieve this in a scalable fashion, agents must be able to relate language to the world and to actions; that is, their understanding of language must be grounded and embodied. However, learning grounded language is a notoriously challenging problem in artificial intelligence research. Here we present an agent that learns to interpret language in a simulated 3D environment where it is rewarded for the successful execution of written instructions. Trained via a combination of reinforcement and unsupervised learning, and beginning with minimal prior knowledge, the agent learns to relate linguistic symbols to emergent perceptual representations of its physical surroundings and to pertinent sequences of actions. The agent's comprehension of language extends beyond its prior experience, enabling it to apply familiar language to unfamiliar situations and to interpret entirely novel instructions. Moreover, the speed with which this agent learns new words increases as its semantic knowledge grows. This facility for generalising and bootstrapping semantic knowledge indicates the potential of the present approach for reconciling ambiguous natural language with the complexity of the physical world.

It is common that a trained classification model is applied to the operating data that is deviated from the training data because of noise. This paper demonstrates that an ensemble classifier, Diversified Multiple Tree (DMT), is more robust in classifying noisy data than other widely used ensemble methods. DMT is tested on three real world biomedical data sets from different laboratories in comparison with four benchmark ensemble classifiers. Experimental results show that DMT is significantly more accurate than other benchmark ensemble classifiers on noisy test data. We also discuss a limitation of DMT and its possible variations.

Despite the fundamental nature of the inhomogeneous Poisson process in the theory and application of stochastic processes, and its attractive generalizations (e.g. Cox process), few tractable nonparametric modeling approaches of intensity functions exist, especially when observed points lie in a high-dimensional space. In this paper we develop a new, computationally tractable Reproducing Kernel Hilbert Space (RKHS) formulation for the inhomogeneous Poisson process. We model the square root of the intensity as an RKHS function. Whereas RKHS models used in supervised learning rely on the so-called representer theorem, the form of the inhomogeneous Poisson process likelihood means that the representer theorem does not apply. However, we prove that the representer theorem does hold in an appropriately transformed RKHS, guaranteeing that the optimization of the penalized likelihood can be cast as a tractable finite-dimensional problem. The resulting approach is simple to implement, and readily scales to high dimensions and large-scale datasets.

Abstract--This paper introduces a family of local feature aggregation functions and a novel method to estimate their parameters, such that they generate optimal representations for classification (or any task that can be expressed as a cost function minimization problem). T o achieve that, we compose the local feature aggregation function with the classifier cost function and we backpropagate the gradient of this cost function in order to update the local feature aggregation function parameters. Experiments on synthetic datasets indicate that our method discovers parameters that model the class-relevant information in addition to the local feature space. Further experiments on a variety of motion and visual descriptors, both on image and video datasets, show that our method outperforms other state-of- the-art local feature aggregation functions, such as Bag of Words, Fisher V ectors and VLAD, by a large margin. A typical image or video classification pipeline, which uses handcrafted features, consists of the following components: local feature extraction (e.g.

We identify conditional parity as a general notion of non-discrimination in machine learning. In fact, several recently proposed notions of non-discrimination, including a few counterfactual notions, are instances of conditional parity. We show that conditional parity is amenable to statistical analysis by studying randomization as a general mechanism for achieving conditional parity and a kernel-based test of conditional parity.

We propose a framework for the linear prediction of a multi-way array (i.e., a tensor) from another multi-way array of arbitrary dimension, using the contracted tensor product. This framework generalizes several existing approaches, including methods to predict a scalar outcome from a tensor, a matrix from a matrix, or a tensor from a scalar. We describe an approach that exploits the multiway structure of both the predictors and the outcomes by restricting the coefficients to have reduced CP-rank. We propose a general and efficient algorithm for penalized least-squares estimation, which allows for a ridge (L_2) penalty on the coefficients. The objective is shown to give the mode of a Bayesian posterior, which motivates a Gibbs sampling algorithm for inference. We illustrate the approach with an application to facial image data. An R package is available at https://github.com/lockEF/MultiwayRegression .

Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the fields like text mining and clickstream data analysis parallelization and the use of cluster architectures becomes important. We present a novel algorithm for fitting regularized generalized linear models in the distributed environment. The algorithm splits data between nodes by features, uses coordinate descent on each node and line search to merge results globally. Convergence proof is provided. A modifications of the algorithm addresses slow node problem. For an important particular case of logistic regression we empirically compare our program with several state-of-the art approaches that rely on different algorithmic and data spitting methods. Experiments demonstrate that our approach is scalable and superior when training on large and sparse datasets.

We propose a nonparametric sequential test that aims to address two practical problems pertinent to online randomized experiments: (i) how to do a hypothesis test for complex metrics; (ii) how to prevent type $1$ error inflation under continuous monitoring. The proposed test does not require knowledge of the underlying probability distribution generating the data. We use the bootstrap to estimate the likelihood for blocks of data followed by mixture sequential probability ratio test. We validate this procedure on data from a major online e-commerce website. We show that the proposed test controls type $1$ error at any time, has good power, is robust to misspecification in the distribution generating the data, and allows quick inference in online randomized experiments.