arXiv subjects

Jose C. Principe

Publications and source records attributed to Jose C. Principe.

At least 55 records · Page 3Linked to original sources

arXiv2020

Unsupervised Foveal Vision Neural Networks with Top-Down Attention

Deep learning architectures are an extremely powerful tool for recognizing and classifying images. However, they require supervised learning and normally work on vectors the size of image pixels and produce the best results when trained on millions of object images. To help mitigate these issues, we propose the fusion of bottom-up saliency and top-down attention employing only unsupervised learning techniques, which helps the object recognition module to focus on relevant data and learn important features that can later be fine-tuned for a specific task. In addition, by utilizing only relevant portions of the data, the training speed can be greatly improved. We test the performance of the proposed Gamma saliency technique on the Toronto and CAT2000 databases, and the foveated vision in the Street View House Numbers (SVHN) database. The results in foveated vision show that Gamma saliency is comparable to the best and computationally faster. The results in SVHN show that our unsupervised cognitive architecture is comparable to fully supervised methods and that the Gamma saliency also improves CNN performance if desired. We also develop a topdown attention mechanism based on the Gamma saliency applied to the top layer of CNNs to improve scene understanding in multi-object images or images with strong background clutter. When we compare the results with human observers in an image dataset of animals occluded in natural scenes, we show that topdown attention is capable of disambiguating object from background and improves system performance beyond the level of human observers.

cs.LG↗

arXiv2020

PRI-VAE: Principle-of-Relevant-Information Variational Autoencoders

Although substantial efforts have been made to learn disentangled representations under the variational autoencoder (VAE) framework, the fundamental properties to the dynamics of learning of most VAE models still remain unknown and under-investigated. In this work, we first propose a novel learning objective, termed the principle-of-relevant-information variational autoencoder (PRI-VAE), to learn disentangled representations. We then present an information-theoretic perspective to analyze existing VAE models by inspecting the evolution of some critical information-theoretic quantities across training epochs. Our observations unveil some fundamental properties associated with VAEs. Empirical results also demonstrate the effectiveness of PRI-VAE on four benchmark data sets.

cs.LG↗

arXiv2020

Understanding Convolutional Neural Networks with Information Theory: An Initial Exploration

The matrix-based Renyi's α-entropy functional and its multivariate extension were recently developed in terms of the normalized eigenspectrum of a Hermitian matrix of the projected data in a reproducing kernel Hilbert space (RKHS). However, the utility and possible applications of these new estimators are rather new and mostly unknown to practitioners. In this paper, we first show that our estimators enable straightforward measurement of information flow in realistic convolutional neural networks (CNN) without any approximation. Then, we introduce the partial information decomposition (PID) framework and develop three quantities to analyze the synergy and redundancy in convolutional layer representations. Our results validate two fundamental data processing inequalities and reveal some fundamental properties concerning the training of CNN.

cs.LG↗

arXiv2020

Fast Estimation of Information Theoretic Learning Descriptors using Explicit Inner Product Spaces

Kernel methods form a theoretically-grounded, powerful and versatile framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the \emph{kernel trick} to perform pairwise evaluations of a kernel function, leading to scalability issues for large datasets due to its linear and superlinear growth with respect to the training data. Recently, we proposed \emph{no-trick} (NT) kernel adaptive filtering (KAF) that leverages explicit feature space mappings using data-independent basis with constant complexity. The inner product defined by the feature mapping corresponds to a positive-definite finite-rank kernel that induces a finite-dimensional reproducing kernel Hilbert space (RKHS). Information theoretic learning (ITL) is a framework where information theory descriptors based on non-parametric estimator of Renyi entropy replace conventional second-order statistics for the design of adaptive systems. An RKHS for ITL defined on a space of probability density functions simplifies statistical inference for supervised or unsupervised learning. ITL criteria take into account the higher-order statistical behavior of the systems and signals as desired. However, this comes at a cost of increased computational complexity. In this paper, we extend the NT kernel concept to ITL for improved information extraction from the signal without compromising scalability. Specifically, we focus on a family of fast, scalable, and accurate estimators for ITL using explicit inner product space (EIPS) kernels. We demonstrate the superior performance of EIPS-ITL estimators and combined NT-KAF using EIPS-ITL cost functions through experiments.

cs.LG↗

arXiv2019

No-Trick (Treat) Kernel Adaptive Filtering using Deterministic Features

Kernel methods form a powerful, versatile, and theoretically-grounded unifying framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the kernel trick to perform pairwise evaluations of a kernel function, which leads to scalability issues for large datasets due to its linear and superlinear growth with respect to the training data. A popular approach to tackle this problem, known as random Fourier features (RFFs), samples from a distribution to obtain the data-independent basis of a higher finite-dimensional feature space, where its dot product approximates the kernel function. Recently, deterministic, rather than random construction has been shown to outperform RFFs, by approximating the kernel in the frequency domain using Gaussian quadrature. In this paper, we view the dot product of these explicit mappings not as an approximation, but as an equivalent positive-definite kernel that induces a new finite-dimensional reproducing kernel Hilbert space (RKHS). This opens the door to no-trick (NT) online kernel adaptive filtering (KAF) that is scalable and robust. Random features are prone to large variances in performance, especially for smaller dimensions. Here, we focus on deterministic feature-map construction based on polynomial-exact solutions and show their superiority over random constructions. Without loss of generality, we apply this approach to classical adaptive filtering algorithms and validate the methodology to show that deterministic features are faster to generate and outperform state-of-the-art kernel methods based on random Fourier features.

cs.LG↗

arXiv2019

Functional Bayesian Filter

We present a general nonlinear Bayesian filter for high-dimensional state estimation using the theory of reproducing kernel Hilbert space (RKHS). Applying kernel method and the representer theorem to perform linear quadratic estimation in a functional space, we derive a Bayesian recursive state estimator for a general nonlinear dynamical system in the original input space. Unlike existing nonlinear extensions of Kalman filter where the system dynamics are assumed known, the state-space representation for the Functional Bayesian Filter (FBF) is completely learned from measurement data in the form of an infinite impulse response (IIR) filter or recurrent network in the RKHS, with universal approximation property. Using positive definite kernel function satisfying Mercer's conditions to compute and evolve information quantities, the FBF exploits both the statistical and time-domain information about the signal, extracts higher-order moments, and preserves the properties of covariances without the ill effects due to conventional arithmetic operations. This novel kernel adaptive filtering algorithm is applied to recurrent network training, chaotic time-series estimation and cooperative filtering using Gaussian and non-Gaussian noises, and inverse kinematics modeling. Simulation results show FBF outperforms existing Kalman-based algorithms.

eess.SP↗

arXiv2019

Algorithmic Design and Implementation of Unobtrusive Multistatic Serial LiDAR Image

To fully understand interactions between marine hydrokinetic (MHK) equipment and marine animals, a fast and effective monitoring system is required to capture relevant information whenever underwater animals appear. A new automated underwater imaging system composed of LiDAR (Light Detection and Ranging) imaging hardware and a scene understanding software module named Unobtrusive Multistatic Serial LiDAR Imager (UMSLI) to supervise the presence of animals near turbines. UMSLI integrates the front end LiDAR hardware and a series of software modules to achieve image preprocessing, detection, tracking, segmentation and classification in a hierarchical manner.

eess.IV↗

arXiv2019

An Exact Reformulation of Feature-Vector-based Radial-Basis-Function Networks for Graph-based Observations

Radial-basis-function networks are traditionally defined for sets of vector-based observations. In this short paper, we reformulate such networks so that they can be applied to adjacency-matrix representations of weighted, directed graphs that represent the relationships between object pairs. We re-state the sum-of-squares objective function so that it is purely dependent on entries from the adjacency matrix. From this objective function, we derive a gradient descent update for the network weights. We also derive a gradient update that simulates the repositioning of the radial basis prototypes and changes in the radial basis prototype parameters. An important property of our radial basis function networks is that they are guaranteed to yield the same responses as conventional radial-basis networks trained on a corresponding vector realization of the relationships encoded by the adjacency-matrix. Such a vector realization only needs to provably exist for this property to hold, which occurs whenever the relationships correspond to distances from some arbitrary metric applied to a latent set of vectors. We therefore completely avoid needing to actually construct vectorial realizations via multi-dimensional scaling, which ensures that the underlying relationships are totally preserved.

cs.LG↗

arXiv2019

Multivariate Extension of Matrix-based Renyi's α-order Entropy Functional

The matrix-based Renyi's α-order entropy functional was recently introduced using the normalized eigenspectrum of a Hermitian matrix of the projected data in a reproducing kernel Hilbert space (RKHS). However, the current theory in the matrix-based Renyi's α-order entropy functional only defines the entropy of a single variable or mutual information between two random variables. In information theory and machine learning communities, one is also frequently interested in multivariate information quantities, such as the multivariate joint entropy and different interactive quantities among multiple variables. In this paper, we first define the matrix-based Renyi's α-order joint entropy among multiple variables. We then show how this definition can ease the estimation of various information quantities that measure the interactions among multiple variables, such as interactive information and total correlation. We finally present an application to feature selection to show how our definition provides a simple yet powerful way to estimate a widely-acknowledged intractable quantity from data. A real example on hyperspectral image (HSI) band selection is also provided.

cs.IT↗

arXiv2019

Correntropy Based Robust Decomposition of Neuromodulations

Neuromodulations as observed in the extracellular electrical potential recordings obtained from Electroencephalograms (EEG) manifest as organized, transient patterns that differ statistically from their featureless noisy background. Leveraging on this statistical dissimilarity, we propose a noniterative robust classification algorithm to isolate, in time, these neuromodulations from the temporally disorganized but structured background activity while simultaneously incorporating temporal sparsity of the events. Specifically, we exploit the ability of correntropy to asses higher - order moments as well as imply the degree of similarity between two random variables in the joint space regulated by the kernel bandwidth. We test our algorithm on DREAMS Sleep Spindle Database and further elaborate on the hyperparameters introduced. Finally, we compare the performance of the algorithm with two algorithms designed on similar ideas; one of which is a quick, simple norm based technique while the other parallels the state-of-the-art Robust Principal Component Analysis (RPCA) to achieve classification. The algorithm is able to match the performance of the state-of-the-art techniques while saving tremendously on computation time and complexity.

eess.SP↗

arXiv2019

Understanding Autoencoders with Information Theoretic Concepts

Despite their great success in practical applications, there is still a lack of theoretical and systematic methods to analyze deep neural networks. In this paper, we illustrate an advanced information theoretic methodology to understand the dynamics of learning and the design of autoencoders, a special type of deep learning architectures that resembles a communication channel. By generalizing the information plane to any cost function, and inspecting the roles and dynamics of different layers using layer-wise information quantities, we emphasize the role that mutual information plays in quantifying learning from data. We further suggest and also experimentally validate, for mean square error training, three fundamental properties regarding the layer-wise flow of information and intrinsic dimensionality of the bottleneck layer, using respectively the data processing inequality and the identification of a bifurcation point in the information plane that is controlled by the given data. Our observations have a direct impact on the optimal design of autoencoders, the design of alternative feedforward training methods, and even in the problem of generalization.

cs.LG↗

arXiv2019

A New Uncertainty Framework for Stochastic Signal Processing

The fields of signal processing and information theory have evolved with the goal of developing formulations to extract intrinsic information from limited amount of data. When one considers the modeling of unpredictably varying processes and complex dynamical signals with a large number of unknowns (such as those encountered in the fields of finance, NLP, communications, etc.), there is a need for algorithms to have increased sensitivity with short spans of data, while maintaining stochastic generalization ability. This naturally calls for an increased focus on localized stochastic representation. So far, most metrics developed for characterizing signals envision data from entropic and probabilistic points of view that lack sensitivity towards quick changes in signal dynamics. We hypothesize that models that work with the intrinsic uncertainties associated with local data induced metric spaces would be significantly more sensitive towards signal characterization. To this end, we develop a new framework for stochastic signal processing that is based on decomposing the local metric space of the signal in a Gaussian Reproducing Kernel Hilbert Space (RKHS). A major advantage of our framework is that we are able to implement this decomposition on a sample-by-sample basis. The key aspects of our framework are the following: (1) We use a data defined metric related to Parzen density estimation for quantifying the local structure of data in the Gaussian RKHS. (2) We use a quantum description of this metric which consequently introduces uncertainty in the structure of the local kernel space. Since the RKHS has been well established and known for providing universal data fitting capabilities, we submit that local quantifiers of the kernel space data projection could significantly improve acquisition of signal information.

eess.SP↗

arXiv2019

Maximum Correntropy Criterion with Variable Center

Correntropy is a local similarity measure defined in kernel space and the maximum correntropy criterion (MCC) has been successfully applied in many areas of signal processing and machine learning in recent years. The kernel function in correntropy is usually restricted to the Gaussian function with center located at zero. However, zero-mean Gaussian function may not be a good choice for many practical applications. In this study, we propose an extended version of correntropy, whose center can locate at any position. Accordingly, we propose a new optimization criterion called maximum correntropy criterion with variable center (MCC-VC). We also propose an efficient approach to optimize the kernel width and center location in MCC-VC. Simulation results of regression with linear in parameters (LIP) models confirm the desirable performance of the new method.

stat.ML↗

arXiv2019

Reduction of Markov Chains using a Value-of-Information-Based Approach

In this paper, we propose an approach to obtain reduced-order models of Markov chains. Our approach is composed of two information-theoretic processes. The first is a means of comparing pairs of stationary chains on different state spaces, which is done via the negative Kullback-Leibler divergence defined on a model joint space. Model reduction is achieved by solving a value-of-information criterion with respect to this divergence. Optimizing the criterion leads to a probabilistic partitioning of the states in the high-order Markov chain. A single free parameter that emerges through the optimization process dictates both the partition uncertainty and the number of state groups. We provide a data-driven means of choosing the `optimal' value of this free parameter, which sidesteps needing to a priori know the number of state groups in an arbitrary chain.

cs.IT↗

arXiv2019

Simple stopping criteria for information theoretic feature selection

Feature selection aims to select the smallest feature subset that yields the minimum generalization error. In the rich literature in feature selection, information theory-based approaches seek a subset of features such that the mutual information between the selected features and the class labels is maximized. Despite the simplicity of this objective, there still remain several open problems in optimization. These include, for example, the automatic determination of the optimal subset size (i.e., the number of features) or a stopping criterion if the greedy searching strategy is adopted. In this paper, we suggest two stopping criteria by just monitoring the conditional mutual information (CMI) among groups of variables. Using the recently developed multivariate matrix-based Renyi's α-entropy functional, which can be directly estimated from data samples, we showed that the CMI among groups of variables can be easily computed without any decomposition or approximation, hence making our criteria easy to implement and seamlessly integrated into any existing information theoretic feature selection methods with a greedy search strategy.

cs.CV↗

arXiv2018

Theory and Algorithms for Pulse Signal Processing

The integrate and fire converter transforms an analog signal into train of biphasic pulses. The pulse train has information encoded in the timing and polarity of pulses. While it has been shown that any finite bandwidth analog signal can be reconstructed from these pulse trains with an error as small as desired, there is a need for fundamental signal processing techniques to operate directly on pulse trains without signal reconstruction. In this paper, the feasibility of performing online the signal processing operations of addition, multiplication, and convolution of analog signals using their pulses train representations is explored. Theoretical framework to perform signal processing with pulse trains imposing minimal restrictions is derived, and algorithms for online implementation of the operators are developed. Performance of the algorithms in processing simulated data is studied. An application of noise subtraction and representation of relevant features of interest in electrocardiogram signal is demonstrated with mean pulse rate less than 20 pulses per second.

eess.SP↗

arXiv2018

Request-and-Reverify: Hierarchical Hypothesis Testing for Concept Drift Detection with Expensive Labels

One important assumption underlying common classification models is the stationarity of the data. However, in real-world streaming applications, the data concept indicated by the joint distribution of feature and label is not stationary but drifting over time. Concept drift detection aims to detect such drifts and adapt the model so as to mitigate any deterioration in the model's predictive performance. Unfortunately, most existing concept drift detection methods rely on a strong and over-optimistic condition that the true labels are available immediately for all already classified instances. In this paper, a novel Hierarchical Hypothesis Testing framework with Request-and-Reverify strategy is developed to detect concept drifts by requesting labels only when necessary. Two methods, namely Hierarchical Hypothesis Testing with Classification Uncertainty (HHT-CU) and Hierarchical Hypothesis Testing with Attribute-wise "Goodness-of-fit" (HHT-AG), are proposed respectively under the novel framework. In experiments with benchmark datasets, our methods demonstrate overwhelming advantages over state-of-the-art unsupervised drift detectors. More importantly, our methods even outperform DDM (the widely used supervised drift detector) when we use significantly fewer labels.

cs.LG↗

arXiv2018

An Analysis of the Value of Information when Exploring Stochastic, Discrete Multi-Armed Bandits

In this paper, we propose an information-theoretic exploration strategy for stochastic, discrete multi-armed bandits that achieves optimal regret. Our strategy is based on the value of information criterion. This criterion measures the trade-off between policy information and obtainable rewards. High amounts of policy information are associated with exploration-dominant searches of the space and yield high rewards. Low amounts of policy information favor the exploitation of existing knowledge. Information, in this criterion, is quantified by a parameter that can be varied during search. We demonstrate that a simulated-annealing-like update of this parameter, with a sufficiently fast cooling schedule, leads to an optimal regret that is logarithmic with respect to the number of episodes.

cs.AI↗