We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point estimation problems without analytical solution (such as hyperparameter or entropy estimation). Despite the large number of available heuristics in the literature, the inherent two-stage sampled nature of the problem makes the theoretical analysis quite challenging, since in practice only samples from sampled distributions are observable, and the estimates have to rely on similarities computed between sets of points. To the best of our knowledge, the only existing technique with consistency guarantees for distribution regression requires kernel density estimation as an intermediate step (which often performs poorly in practice), and the domain of the distributions to be compact Euclidean. In this paper, we study a simple, analytically computable, ridge regression-based alternative to distribution regression, where we embed the distributions to a reproducing kernel Hilbert space, and learn the regressor from the embeddings to the outputs. Our main contribution is to prove that this scheme is consistent in the two-stage sampled setup under mild conditions (on separable topological domains enriched with kernels): we present an exact computational-statistical efficiency trade-off analysis showing that our estimator is able to match the one-stage sampled minimax optimal rate [Caponnetto and De Vito, 2007; Steinwart et al., 2009]. This result answers a 17-year-old open question, establishing the consistency of the classical set kernel [Haussler, 1999; Gaertner et. al, 2002] in regression. We also cover consistency for more recent kernels on distributions, including those due to [Christmann and Steinwart, 2010].

Body-worn video (BWV) cameras are increasingly utilized by police departments to provide a record of police-public interactions. However, large-scale BWV deployment produces terabytes of data per week, necessitating the development of effective computational methods to identify salient changes in video. In work carried out at the 2016 RIPS program at IPAM, UCLA, we present a novel two-stage framework for video change-point detection. First, we employ state-of-the-art machine learning methods including convolutional neural networks and support vector machines for scene classification. We then develop and compare change-point detection algorithms utilizing mean squared-error minimization, forecasting methods, hidden Markov models, and maximum likelihood estimation to identify noteworthy changes. We test our framework on detection of vehicle exits and entrances in a BWV data set provided by the Los Angeles Police Department and achieve over 90% recall and nearly 70% precision -- demonstrating robustness to rapid scene changes, extreme luminance differences, and frequent camera occlusions.

Generating user interpretable multi-class predictions in data rich environments with many classes and explanatory covariates is a daunting task. We introduce Diagonal Orthant Latent Dirichlet Allocation (DOLDA), a supervised topic model for multi-class classification that can handle both many classes as well as many covariates. To handle many classes we use the recently proposed Diagonal Orthant (DO) probit model (Johndrow et al., 2013) together with an efficient Horseshoe prior for variable selection/shrinkage (Carvalho et al., 2010). We propose a computationally efficient parallel Gibbs sampler for the new model. An important advantage of DOLDA is that learned topics are directly connected to individual classes without the need for a reference class. We evaluate the model's predictive accuracy on two datasets and demonstrate DOLDA's advantage in interpreting the generated predictions.

Image Forensics has already achieved great results for the source camera identification task on images. Standard approaches for data coming from Social Network Platforms cannot be applied due to different processes involved (e.g., scaling, compression, etc.). Over 1 billion images are shared each day on the Internet and obtaining information about their history from the moment they were acquired could be exploited for investigation purposes. In this paper, a classification engine for the reconstruction of the history of an image, is presented. Specifically, exploiting K-NN and decision trees classifiers and a-priori knowledge acquired through image analysis, we propose an automatic approach that can understand which Social Network Platform has processed an image and the software application used to perform the image upload. The engine makes use of proper alterations introduced by each platform as features. Results, in terms of global accuracy on a dataset of 2720 images, confirm the effectiveness of the proposed strategy.

In this paper, we consider linear state-space models with compressible innovations and convergent transition matrices in order to model spatiotemporally sparse transient events. We perform parameter and state estimation using a dynamic compressed sensing framework and develop an efficient solution consisting of two nested Expectation-Maximization (EM) algorithms. Under suitable sparsity assumptions on the innovations, we prove recovery guarantees and derive confidence bounds for the state estimates. We provide simulation studies as well as application to spike deconvolution from calcium imaging data which verify our theoretical results and show significant improvement over existing algorithms.

Structural equation models (SEMs) and vector autoregressive models (VARMs) are two broad families of approaches that have been shown useful in effective brain connectivity studies. While VARMs postulate that a given region of interest in the brain is directionally connected to another one by virtue of time-lagged influences, SEMs assert that causal dependencies arise due to contemporaneous effects, and may even be adopted when nodal measurements are not necessarily multivariate time series. To unify these complementary perspectives, linear structural vector autoregressive models (SVARMs) that leverage both contemporaneous and time-lagged nodal data have recently been put forth. Albeit simple and tractable, linear SVARMs are quite limited since they are incapable of modeling nonlinear dependencies between neuronal time series. To this end, the overarching goal of the present paper is to considerably broaden the span of linear SVARMs by capturing nonlinearities through kernels, which have recently emerged as a powerful nonlinear modeling framework in canonical machine learning tasks, e.g., regression, classification, and dimensionality reduction. The merits of kernel-based methods are extended here to the task of learning the effective brain connectivity, and an efficient regularized estimator is put forth to leverage the edge sparsity inherent to real-world complex networks. Judicious kernel choice from a preselected dictionary of kernels is also addressed using a data-driven approach. Extensive numerical tests on ECoG data captured through a study on epileptic seizures demonstrate that it is possible to unveil previously unknown causal links between brain regions of interest.

Machine-learning provides a theoretical framework for the discovery and prioritization of bioactive compounds with desired pharmacological effects and their optimization as drug-like leads. Biological target identification and protein design are emerging areas of application. Among the many machine-learning approaches in molecular informatics, chemocentric methods have found widespread application. Their underlying logic typically follows three steps. First, there is the selection of a problem-specific set of descriptors that are believed to capture the essential properties of the molecules involved.

Then we use another map transformation, which will apply the ParseObs function to transform each Array of Double in the RDD into an Array of Cancer Observation objects. The toDF() method transforms the RDD of Array[[Cancer Observation]] into a Dataframe with the Cancer Observation class schema. Below the data is split into a training data set and a test data set, 70% of the data is used to train the model, and 30% will be used for testing. In this blog post, we showed you how to get started using Apache Spark's machine learning Logistic Regression for classification.

Hidden Decision Trees is a statistical and data mining methodology (just like logistic regression, SVM, neural networks or decision trees) to handle problems with large amounts of data, non-linearities and strongly correlated dependent variables. The technique is easy to implement in any programming language. It is more robust than decision trees or logistic regression, and help detect natural final nodes. Implementations typically rely heavily on large, granular hash tables. No decision tree is actually built (thus the name hidden decision trees), but the final output of an hidden decision tree procedure consists of a few hundred nodes from multiple non-overlapping small decision trees.

In pattern recognition, the K-Nearest Neighbor algorithm (KNN) is a method for classifying objects based on the closest training examples in the feature space. KNN is a type of instance-based learning, or lazy learning where the function is only approximated locally and all computation is deferred until classification. The KNN algorithm is amongst the simplest of all machine learning algorithms: an object is classified by a majority vote of its neighbors, with the object being assigned to the class most common amongst its k nearest neighbors (k is a positive integer, typically small). If k 1, then the object is simply assigned to the class of its nearest neighbor [Source: Wikipedia]. In today's post, we explore the application of KNN to an automobile manufacturer that has developed prototypes for two new vehicles, a car and a truck.