Many machine learning algorithms require precise estimates of covariance matrices. The sample covariance matrix performs poorly in high-dimensional settings, which has stimulated the development of alternative methods, the majority based on factor models and shrinkage. Recent work of Ledoit and Wolf has extended the shrinkage framework to Nonlinear Shrinkage (NLS), a more powerful covariance estimator based on Random Matrix Theory. Our contribution shows that, contrary to claims in the literature, cross-validation based covariance matrix estimation (CVC) yields comparable performance at strongly reduced complexity and runtime. On two real world data sets, we show that the CVC estimator yields superior results than competing shrinkage and factor based methods.

Kernel dependence measures yield accurate estimates of nonlinear relations between random variables, and they are also endorsed with solid theoretical properties and convergence rates. Besides, the empirical estimates are easy to compute in closed form just involving linear algebra operations. However, they are hampered by two important problems: the high computational cost involved, as two kernel matrices of the sample size have to be computed and stored, and the interpretability of the measure, which remains hidden behind the implicit feature map. We here address these two issues. We introduce the Sensitivity Maps (SMs) for the Hilbert-Schmidt independence criterion (HSIC). Sensitivity maps allow us to explicitly analyze and visualize the relative relevance of both examples and features on the dependence measure. We also present the randomized HSIC (RHSIC) and its corresponding sensitivity maps to cope with large scale problems. We build upon the framework of random features and the Bochner's theorem to approximate the involved kernels in the canonical HSIC. The power of the RHSIC measure scales favourably with the number of samples, and it approximates HSIC and the sensitivity maps efficiently. Convergence bounds of both the measure and the sensitivity map are also provided. Our proposal is illustrated in synthetic examples, and challenging real problems of dependence estimation, feature selection, and causal inference from empirical data.

Genetic sequence data are well described by hidden Markov models (HMMs) in which latent states correspond to clusters of similar mutation patterns. Theory from statistical genetics suggests that these HMMs are nonhomogeneous (their transition probabilities vary along the chromosome) and have large support for self transitions. We develop a new nonparametric model of genetic sequence data, based on the hierarchical Dirichlet process, which supports these self transitions and nonhomogeneity. Our model provides a parameterization of the genetic process that is more parsimonious than other more general nonparametric models which have previously been applied to population genetics. We provide truncation-free MCMC inference for our model using a new auxiliary sampling scheme for Bayesian nonparametric HMMs. In a series of experiments on male X chromosome data from the Thousand Genomes Project and also on data simulated from a population bottleneck we show the benefits of our model over the popular finite model fastPHASE, which can itself be seen as a parametric truncation of our model. We find that the number of HMM states found by our model is correlated with the time to the most recent common ancestor in population bottlenecks. This work demonstrates the flexibility of Bayesian nonparametrics applied to large and complex genetic data.

We trained on each acoustic feature a full covariance, genderindependent UBM model with 2048 Gaussians followed by a 600-dimensional i-vector extractor to establish our MFCCand PLP-based i-vector systems. The unlabeled set of development data was used in the training of both the UBM and the i-vector extractor. The open-source Kaldi software has been used for all these processing steps [20]. It has been shown that successive acoustic observation vectors tend to be highly correlated. This may be problematic for maximum a posteriori (MAP) estimation of i-vectors. To investigating this issue, scaling the zero and first order Baum-Welch statistics before presenting them to the i-vector extractor has been proposed. It turns out that a scale factor of 0.33 gives a slight edge, resulting in a better decision cost function [10]. This scaling factor has been performed in training the i-vector extractor as well as in the testing.

Deep kernel learning combines the non-parametric flexibility of kernel methods with the inductive biases of deep learning architectures. We propose a novel deep kernel learning model and stochastic variational inference procedure which generalizes deep kernel learning approaches to enable classification, multi-task learning, additive covariance structures, and stochastic gradient training. Specifically, we apply additive base kernels to subsets of output features from deep neural architectures, and jointly learn the parameters of the base kernels and deep network through a Gaussian process marginal likelihood objective. Within this framework, we derive an efficient form of stochastic variational inference which leverages local kernel interpolation, inducing points, and structure exploiting algebra. We show improved performance over stand alone deep networks, SVMs, and state of the art scalable Gaussian processes on several classification benchmarks, including an airline delay dataset containing 6 million training points, CIFAR, and ImageNet.

In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of reproducing kernel Hilbert space theory to learn from such functional data. Basic concepts and properties of kernel-based learning are extended to include the estimation of function-valued functions. In this setting, the representer theorem is restated, a set of rigorously defined infinite-dimensional operator-valued kernels that can be valuably applied when the data are functions is described, and a learning algorithm for nonlinear functional data analysis is introduced. The methodology is illustrated through speech and audio signal processing experiments.

Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing constraints on covariance, one can ensure consistency of linear response with the variational parameters, and in so doing inference of marginal probability distributions is improved. For the Bethe approximation and its generalizations, improvements are achieved with simple choices of the constraints. The approximations are presented as variational frameworks; iterative procedures related to message passing are provided for finding the minima.

This article is part of an MIT SMR initiative exploring how technology is reshaping the practice of management. The paradox of automation: Earlier this year, Facebook exorcised those pesky human editors who were introducing political bias into its Trending news list and left the job to algorithms. Now, reports Caitlin Dewey in The Washington Post, the Trending news isn't biased, but some of it is fake. Turns out the algorithms can't tell a real news story from a hoax. Facebook says it can improve its algorithms, but errors of judgment aren't the only pitfall in transferring human tasks to machines.

An artificial intelligence (AI) judge has accurately predicted most verdicts of the European Court of Human Rights, and might soon be making important decisions about cases. Scientists built an artificial intelligence computer that was able to look at legal evidence as well as considering ethical questions to decide how a case should be decided. And it predicted those with 79 per cent accuracy, according to its creators. The algorithm looked at data sets made up 584 cases relating to torture and degrading treatment, fair trials and privacy. The computer was able to look through that information and make its own decision – which lined up with those made by Europe's most senior judges in almost every case.

Bullying has recently become a hot topic of conversation, particularly in schools. But of course, it's been an issue for decades, if not millennia, probably because it's human nature to pick on others who are seen as weak or different. Sadly, a new study suggests that we may not limit our bullying to other humans. In the dawning age of artificial intelligence–like the kind found in self-driving cars–we may begin to bully software. The study was conducted by Goodyear and the London School of Economics.