Viewing a data set such as the clouds of Jupiter, coherence is readily apparent to human observers, especially the Great Red Spot, but also other great storms and persistent structures. There are now many different definitions and perspectives mathematically describing coherent structures, but we will take an image processing perspective here. We describe an image processing perspective inference of coherent sets from a fluidic system directly from image data, without attempting to first model underlying flow fields, related to a concept in image processing called motion tracking. In contrast to standard spectral methods for image processing which are generally related to a symmetric affinity matrix, leading to standard spectral graph theory, we need a not symmetric affinity which arises naturally from the underlying arrow of time. We develop an anisotropic, directed diffusion operator corresponding to flow on a directed graph, from a directed affinity matrix developed with coherence in mind, and corresponding spectral graph theory from the graph Laplacian. Our methodology is not offered as more accurate than other traditional methods of finding coherent sets, but rather our approach works with alternative kinds of data sets, in the absence of vector field. Our examples will include partitioning the weather and cloud structures of Jupiter, and a local to Potsdam, N.Y. lake-effect snow event on Earth, as well as the benchmark test double-gyre system.

Machine learning has become an important component for many systems and applications including computer vision, spam filtering, malware and network intrusion detection, among others. Despite the capabilities of machine learning algorithms to extract valuable information from data and produce accurate predictions, it has been shown that these algorithms are vulnerable to attacks. Data poisoning is one of the most relevant security threats against machine learning systems, where attackers can subvert the learning process by injecting malicious samples in the training data. Recent work in adversarial machine learning has shown that the so-called optimal attack strategies can successfully poison linear classifiers, degrading the performance of the system dramatically after compromising a small fraction of the training dataset. In this paper we propose a defence mechanism to mitigate the effect of these optimal poisoning attacks based on outlier detection. We show empirically that the adversarial examples generated by these attack strategies are quite different from genuine points, as no detectability constrains are considered to craft the attack. Hence, they can be detected with an appropriate pre-filtering of the training dataset.

If you wanted to classify animals, for example, based on a plethora of relevant collected data, you would quickly find that all sorts of potential data attributes, or features, were relatively unhelpful for classification. For example, given that most living creatures have precisely 1 heart, this particular feature would not be beneficial, from a learning perspective. On the other hand, an attribute denoting whether or not a given animal is hoofed would likely be a powerful predictor. Further, using all of these irrelevant attributes, mixed in with the powerful predictors, may actually have a negative effect on the resulting model. This is to say nothing of the increased training times that may come along with the inclusion of useless attributes, or the overfitting which may occur on the training data.

It was the week of Christmas in 1989 in Amsterdam, 48* F and cloudy, when Guido van Rossum started tinkering on a small project to busy himself while his employer's office closed for the holiday. He placed a high emphasis on readability and uniformity in an era that praised languages like C and Perl (PHP's high-maintenance personality would crash the party later). The result was a gorgeously elegant open source language named after Monty Python's Flying Circus. Since its official release in 1993, Python has displayed its prowess across multiple industries and in widely varying use cases. It is now the most widely taught introductory language in the top computer science programs worldwide, was named the most in-demand programming language in the U.S. by Forbes' fintech columnist, and hit #2 on the list of most GitHub pulls by language in 2017.

In the paper, we study the mini-batch stochastic ADMMs (alternating direction method of multipliers) for the nonconvex nonsmooth optimization. We prove that, given an appropriate mini-batch size, the mini-batch stochastic ADMM without variance reduction (VR) technique is convergent and reaches the convergence rate of $O(1/T)$ to obtain a stationary point of the nonconvex optimization, where $T$ denotes the number of iterations. Moreover, we extend the mini-batch stochastic gradient method to both the nonconvex SVRG-ADMM and SAGA-ADMM in our initial paper \citep{huang2016stochastic}, and also prove that these mini-batch stochastic ADMMs reach the convergence rate of $O(1/T)$ without the condition on the mini-batch size. In particular, we provide a specific parameter selection for step size $\eta$ of stochastic gradients and penalization parameter $\rho$ of the augmented Lagrangian function. Finally, some experimental results demonstrate the effectiveness of our algorithms.

We give the first provably efficient algorithm for learning a one hidden layer convolutional network with respect to a general class of (potentially overlapping) patches. Additionally, our algorithm requires only mild conditions on the underlying distribution. We prove that our framework captures commonly used schemes from computer vision, including one-dimensional and two-dimensional "patch and stride" convolutions. Our algorithm-- $Convotron$ -- is inspired by recent work applying isotonic regression to learning neural networks. Convotron uses a simple, iterative update rule that is stochastic in nature and tolerant to noise (requires only that the conditional mean function is a one layer convolutional network, as opposed to the realizable setting). In contrast to gradient descent, Convotron requires no special initialization or learning-rate tuning to converge to the global optimum. We also point out that learning one hidden convolutional layer with respect to a Gaussian distribution and just $one$ disjoint patch $P$ (the other patches may be arbitrary) is $easy$ in the following sense: Convotron can efficiently recover the hidden weight vector by updating $only$ in the direction of $P$.

While it's always possible to compute a variational approximation to a posterior distribution, it can be difficult to discover problems with this approximation". We propose two diagnostic algorithms to alleviate this problem. The Pareto-smoothed importance sampling (PSIS) diagnostic gives a goodness of fit measurement for joint distributions, while simultaneously improving the error in the estimate.

We propose a family of variational approximations to Bayesian posterior distributions, called $\alpha$-VB, with provable statistical guarantees. The standard variational approximation is a special case of $\alpha$-VB with $\alpha=1$. When $\alpha \in(0,1]$, a novel class of variational inequalities are developed for linking the Bayes risk under the variational approximation to the objective function in the variational optimization problem, implying that maximizing the evidence lower bound in variational inference has the effect of minimizing the Bayes risk within the variational density family. Operating in a frequentist setup, the variational inequalities imply that point estimates constructed from the $\alpha$-VB procedure converge at an optimal rate to the true parameter in a wide range of problems. We illustrate our general theory with a number of examples, including the mean-field variational approximation to (low)-high-dimensional Bayesian linear regression with spike and slab priors, mixture of Gaussian models, latent Dirichlet allocation, and (mixture of) Gaussian variational approximation in regular parametric models.

This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian processes (GP), that does not rely on linearizations or unimodal Gaussian approximations of the belief. The algorithm can be seen as a combination of a sampling-based filter and a probabilistic Bayes filter. GP-SUM operates by sampling the state distribution and propagating each sample through the dynamic system and observation models. Effective sampling and accurate probabilistic propagation are possible by relying on the GP form of the system, and a Gaussian mixture form of the belief. We show that GP-SUM outperforms several GP-Bayes and Particle Filters on a standard benchmark. We also illustrate its practical use in a pushing task, and demonstrate that it predicts heteroscedasticity, i.e., different amounts of uncertainty, and multi-modality when naturally occurring in pushing.

The immense amount of daily generated and communicated data presents unique challenges in their processing. Clustering, the grouping of data without the presence of ground-truth labels, is an important tool for drawing inferences from data. Subspace clustering (SC) is a relatively recent method that is able to successfully classify nonlinearly separable data in a multitude of settings. In spite of their high clustering accuracy, SC methods incur prohibitively high computational complexity when processing large volumes of high-dimensional data. Inspired by random sketching approaches for dimensionality reduction, the present paper introduces a randomized scheme for SC, termed Sketch-SC, tailored for large volumes of high-dimensional data. Sketch-SC accelerates the computationally heavy parts of state-of-the-art SC approaches by compressing the data matrix across both dimensions using random projections, thus enabling fast and accurate large-scale SC. Performance analysis as well as extensive numerical tests on real data corroborate the potential of Sketch-SC and its competitive performance relative to state-of-the-art scalable SC approaches.