Video analytics requires operating with large amounts of data. Compressive sensing allows to reduce the number of measurements required to represent the video using the prior knowledge of sparsity of the original signal, but it imposes certain conditions on the design matrix. The Bayesian compressive sensing approach relaxes the limitations of the conventional approach using the probabilistic reasoning and allows to include different prior knowledge about the signal structure. This paper presents two Bayesian compressive sensing methods for autonomous object detection in a video sequence from a static camera. Their performance is compared on the real datasets with the non-Bayesian greedy algorithm. It is shown that the Bayesian methods can provide the same accuracy as the greedy algorithm but much faster; or if the computational time is not critical they can provide more accurate results.

One of the most challenging tasks when adopting Bayesian Networks (BNs) is the one of learning their structure from data. This task is complicated by the huge search space of possible solutions and turned out to be a well-known NP-hard problem and, hence, approximations are required. However, to the best of our knowledge, a quantitative analysis of the performance and characteristics of the different heuristics to solve this problem has never been done before. For this reason, in this work, we provide a detailed study of the different state-of-the-arts methods for structural learning on simulated data considering both BNs with discrete and continuous variables, and with different rates of noise in the data. In particular, we investigate the characteristics of different widespread scores proposed for the inference and the statistical pitfalls within them.

Representations are fundamental to artificial intelligence. The performance of a learning system depends on the type of representation used for representing the data. Typically, these representations are hand-engineered using domain knowledge. More recently, the trend is to learn these representations through stochastic gradient descent in multi-layer neural networks, which is called backprop. Learning the representations directly from the incoming data stream reduces the human labour involved in designing a learning system. More importantly, this allows in scaling of a learning system for difficult tasks. In this paper, we introduce a new incremental learning algorithm called crossprop, which learns incoming weights of hidden units based on the meta-gradient descent approach, that was previously introduced by Sutton (1992) and Schraudolph (1999) for learning step-sizes. The final update equation introduces an additional memory parameter for each of these weights and generalizes the backprop update equation. From our experiments, we show that crossprop learns and reuses its feature representation while tackling new and unseen tasks whereas backprop relearns a new feature representation.

Learning DAG or Bayesian network models is an important problem in multi-variate causal inference. However, a number of challenges arises in learning large-scale DAG models including model identifiability and computational complexity since the space of directed graphs is huge. In this paper, we address these issues in a number of steps for a broad class of DAG models where the noise or variance is signal-dependent. Firstly we introduce a new class of identifiable DAG models, where each node has a distribution where the variance is a quadratic function of the mean (QVF DAG models). Our QVF DAG models include many interesting classes of distributions such as Poisson, Binomial, Geometric, Exponential, Gamma and many other distributions in which the noise variance depends on the mean. We prove that this class of QVF DAG models is identifiable, and introduce a new algorithm, the OverDispersion Scoring (ODS) algorithm, for learning large-scale QVF DAG models. Our algorithm is based on firstly learning the moralized or undirected graphical model representation of the DAG to reduce the DAG search-space, and then exploiting the quadratic variance property to learn the causal ordering. We show through theoretical results and simulations that our algorithm is statistically consistent in the high-dimensional p>n setting provided that the degree of the moralized graph is bounded and performs well compared to state-of-the-art DAG-learning algorithms.

A Siamese Deep Forest (SDF) is proposed in the paper. It is based on the Deep Forest or gcForest proposed by Zhou and Feng and can be viewed as a gcForest modification. It can be also regarded as an alternative to the well-known Siamese neural networks. The SDF uses a modified training set consisting of concatenated pairs of vectors. Moreover, it defines the class distributions in the deep forest as the weighted sum of the tree class probabilities such that the weights are determined in order to reduce distances between similar pairs and to increase them between dissimilar points. We show that the weights can be obtained by solving a quadratic optimization problem. The SDF aims to prevent overfitting which takes place in neural networks when only limited training data are available. The numerical experiments illustrate the proposed distance metric method.

In the recent years, we have witnessed the development of multi-label classification methods which utilize the structure of the label space in a divide and conquer approach to improve classification performance and allow large data sets to be classified efficiently. Yet most of the available data sets have been provided in train/test splits that did not account for maintaining a distribution of higher-order relationships between labels among splits or folds. We present a new approach to stratifying multi-label data for classification purposes based on the iterative stratification approach proposed by Sechidis et. al. in an ECML PKDD 2011 paper. Our method extends the iterative approach to take into account second-order relationships between labels. Obtained results are evaluated using statistical properties of obtained strata as presented by Sechidis. We also propose new statistical measures relevant to second-order quality: label pairs distribution, the percentage of label pairs without positive evidence in folds and label pair - fold pairs that have no positive evidence for the label pair. We verify the impact of new methods on classification performance of Binary Relevance, Label Powerset and a fast greedy community detection based label space partitioning classifier. Random Forests serve as base classifiers. We check the variation of the number of communities obtained per fold, and the stability of their modularity score. Second-Order Iterative Stratification is compared to standard k-fold, label set, and iterative stratification. The proposed approach lowers the variance of classification quality, improves label pair oriented measures and example distribution while maintaining a competitive quality in label-oriented measures. We also witness an increase in stability of network characteristics.

We establish a full relationship between Kalman filtering and Amari's natural gradient in statistical learning. Namely, using an online natural gradient descent on data log-likelihood to evaluate the parameter of a probabilistic model from a series of observations, is exactly equivalent to using an extended Kalman filter to estimate the parameter (assumed to have constant dynamics). In the i.i.d. case, this relation is a consequence of the "information filter" phrasing of the extended Kalman filter. In the recurrent (state space, non-i.i.d.) case, we prove that the joint Kalman filter over states and parameters is a natural gradient on top of real-time recurrent learning (RTRL), a classical algorithm to train recurrent models. This exact algebraic correspondence provides relevant settings for natural gradient hyperparameters such as learning rates or initialization and regularization of the Fisher information matrix.

This paper focuses on the estimation of the sample covariance matrix from low-dimensional random projections of data known as compressive measurements. In particular, we present an unbiased estimator to extract the covariance structure from compressive measurements obtained by a general class of random projection matrices consisting of i.i.d. zero-mean entries and finite first four moments. In contrast to previous works, we make no structural assumptions about the underlying covariance matrix such as being low-rank. In fact, our analysis is based on a non-Bayesian data setting which requires no distributional assumptions on the set of data samples. Furthermore, inspired by the generality of the projection matrices, we propose an approach to covariance estimation that utilizes sparse Rademacher matrices. Therefore, our algorithm can be used to estimate the covariance matrix in applications with limited memory and computation power at the acquisition devices. Experimental results demonstrate that our approach allows for accurate estimation of the sample covariance matrix on several real-world data sets, including video data.

Integrated Computational Materials Engineering (ICME) aims to accelerate optimal design of complex material systems by integrating material science and design automation. For tractable ICME, it is required that (1) a structural feature space be identified to allow reconstruction of new designs, and (2) the reconstruction process be property-preserving. The majority of existing structural presentation schemes rely on the designer's understanding of specific material systems to identify geometric and statistical features, which could be biased and insufficient for reconstructing physically meaningful microstructures of complex material systems. In this paper, we develop a feature learning mechanism based on convolutional deep belief network to automate a two-way conversion between microstructures and their lower-dimensional feature representations, and to achieves a 1000-fold dimension reduction from the microstructure space. The proposed model is applied to a wide spectrum of heterogeneous material systems with distinct microstructural features including Ti-6Al-4V alloy, Pb63-Sn37 alloy, Fontainebleau sandstone, and Spherical colloids, to produce material reconstructions that are close to the original samples with respect to 2-point correlation functions and mean critical fracture strength. This capability is not achieved by existing synthesis methods that rely on the Markovian assumption of material microstructures.

We investigate the 3-architecture Connected Facility Location Problem arising in the design of urban telecommunication access networks. We propose an original optimization model for the problem that includes additional variables and constraints to take into account wireless signal coverage. Since the problem can prove challenging even for modern state-of-the art optimization solvers, we propose to solve it by an original primal heuristic which combines a probabilistic fixing procedure, guided by peculiar Linear Programming relaxations, with an exact MIP heuristic, based on a very large neighborhood search. Computational experiments on a set of realistic instances show that our heuristic can find solutions associated with much lower optimality gaps than a state-of-the-art solver.