arXiv subjects

Jose C. Principe

Publications and source records attributed to Jose C. Principe.

At least 19 recordsLinked to original sources

arXiv2026

MLE-UVAD: Minimal Latent Entropy Autoencoder for Fully Unsupervised Video Anomaly Detection

In this paper, we address the challenging problem of single-scene, fully unsupervised video anomaly detection (VAD), where raw videos containing both normal and abnormal events are used directly for training and testing without any labels. This differs sharply from prior work that either requires extensive labeling (fully or weakly supervised) or depends on normal-only videos (one-class classification), which are vulnerable to distribution shifts and contamination. We propose an entropy-guided autoencoder that detects anomalies through reconstruction error by reconstructing normal frames well while making anomalies reconstruct poorly. The key idea is to combine the standard reconstruction loss with a novel Minimal Latent Entropy (MLE) loss in the autoencoder. Reconstruction loss alone maps normal and abnormal inputs to distinct latent clusters due to their inherent differences, but also risks reconstructing anomalies too well to detect. Therefore, MLE loss addresses this by minimizing the entropy of latent embeddings, encouraging them to concentrate around high-density regions. Since normal frames dominate the raw video, sparse anomalous embeddings are pulled into the normal cluster, so the decoder emphasizes normal patterns and produces poor reconstructions for anomalies. This dual-loss design produces a clear reconstruction gap that enables effective anomaly detection. Extensive experiments on two widely used benchmarks and a challenging self-collected driving dataset demonstrate that our method achieves robust and superior performance over baselines.

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arXiv2025

Contrastive Entropy Bounds for Density and Conditional Density Decomposition

This paper studies the interpretability of neural network features from a Bayesian Gaussian view, where optimizing a cost is reaching a probabilistic bound; learning a model approximates a density that makes the bound tight and the cost optimal, often with a Gaussian mixture density. The two examples are Mixture Density Networks (MDNs) using the bound for the marginal and autoencoders using the conditional bound. It is a known result, not only for autoencoders, that minimizing the error between inputs and outputs maximizes the dependence between inputs and the middle. We use Hilbert space and decomposition to address cases where a multiple-output network produces multiple centers defining a Gaussian mixture. Our first finding is that an autoencoder's objective is equivalent to maximizing the trace of a Gaussian operator, the sum of eigenvalues under bases orthonormal w.r.t. the data and model distributions. This suggests that, when a one-to-one correspondence as needed in autoencoders is unnecessary, we can instead maximize the nuclear norm of this operator, the sum of singular values, to maximize overall rank rather than trace. Thus the trace of a Gaussian operator can be used to train autoencoders, and its nuclear norm can be used as divergence to train MDNs. Our second test uses inner products and norms in a Hilbert space to define bounds and costs. Such bounds often have an extra norm compared to KL-based bounds, which increases sample diversity and prevents the trivial solution where a multiple-output network produces the same constant, at the cost of requiring a sample batch to estimate and optimize. We propose an encoder-mixture-decoder architecture whose decoder is multiple-output, producing multiple centers per sample, potentially tightening the bound. Assuming the data are small-variance Gaussian mixtures, this upper bound can be tracked and analyzed quantitatively.

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arXiv2025

A Closed-Form Solution for Kernel Adaptive Filtering

Unlike the conventional kernel adaptive filtering (KAF) approach of using a fixed kernel to define the Reproducing Kernel Hilbert Space (RKHS), this paper embeds the statistics of the input data in the kernel definition, obtaining a closed-form solution for nonlinear adaptive filtering. We call this solution the Functional Wiener Filter (FWF), and it is formally an extension of Parzen's work on the autocorrelation RKHS to nonlinear functional spaces. We present a method for approximating the FWF in an explicit, finite-dimensional RKHS to model time series directly from realizations, which is less computationally demanding at test time than other KAF methods. We show that FWF outperforms KAF on a synthetic dataset that meets the conditions of the theory, and is comparable to other KAF algorithms for both a chaotic and real-world time series. We demonstrate how the difference equation learned by the FWF can be extracted, leading to possible applications in system identification.

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arXiv2025

A Simple and Effective Method for Uncertainty Quantification and OOD Detection

Bayesian neural networks and deep ensemble methods have been proposed for uncertainty quantification; however, they are computationally intensive and require large storage. By utilizing a single deterministic model, we can solve the above issue. We propose an effective method based on feature space density to quantify uncertainty for distributional shifts and out-of-distribution (OOD) detection. Specifically, we leverage the information potential field derived from kernel density estimation to approximate the feature space density of the training set. By comparing this density with the feature space representation of test samples, we can effectively determine whether a distributional shift has occurred. Experiments were conducted on a 2D synthetic dataset (Two Moons and Three Spirals) as well as an OOD detection task (CIFAR-10 vs. SVHN). The results demonstrate that our method outperforms baseline models.

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arXiv2025

Spectral Eigenfunction Decomposition for Kernel Adaptive Filtering

Kernel adaptive filtering (KAF) integrates traditional linear algorithms with kernel methods to generate nonlinear solutions in the input space. The standard approach relies on the representer theorem and the kernel trick to perform pairwise evaluations of a kernel function in place of the inner product, which leads to scalability issues for large datasets due to its linear and superlinear growth with respect to the size of the training data. Explicit features have been proposed to tackle this problem, exploiting the properties of the Gaussian-type kernel functions. These approximation methods address the implicitness and infinite dimensional representation of conventional kernel methods. However, achieving an accurate finite approximation for the kernel evaluation requires a sufficiently large vector representation for the dot products. An increase in the input-space dimension leads to a combinatorial explosion in the dimensionality of the explicit space, i.e., it trades one dimensionality problem (implicit, infinite dimensional RKHS) for another (curse of dimensionality). This paper introduces a construction that simultaneously solves these two problems in a principled way, by providing an explicit Euclidean representation of the RKHS while reducing its dimensionality. We present SPEctral Eigenfunction Decomposition (SPEED) along with an efficient incremental approach for fast calculation of the dominant kernel eigenbasis, which enables us to track the kernel eigenspace dynamically for adaptive filtering. Simulation results on chaotic time series prediction demonstrate this novel construction outperforms existing explicit kernel features with greater efficiency.

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arXiv2024

Learning Cortico-Muscular Dependence through Orthonormal Decomposition of Density Ratios

The cortico-spinal neural pathway is fundamental for motor control and movement execution, and in humans it is typically studied using concurrent electroencephalography (EEG) and electromyography (EMG) recordings. However, current approaches for capturing high-level and contextual connectivity between these recordings have important limitations. Here, we present a novel application of statistical dependence estimators based on orthonormal decomposition of density ratios to model the relationship between cortical and muscle oscillations. Our method extends from traditional scalar-valued measures by learning eigenvalues, eigenfunctions, and projection spaces of density ratios from realizations of the signal, addressing the interpretability, scalability, and local temporal dependence of cortico-muscular connectivity. We experimentally demonstrate that eigenfunctions learned from cortico-muscular connectivity can accurately classify movements and subjects. Moreover, they reveal channel and temporal dependencies that confirm the activation of specific EEG channels during movement. Our code is available at https://github.com/bohu615/corticomuscular-eigen-encoder.

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arXiv2024

ELEMENT: Episodic and Lifelong Exploration via Maximum Entropy

This paper proposes \emph{Episodic and Lifelong Exploration via Maximum ENTropy} (ELEMENT), a novel, multiscale, intrinsically motivated reinforcement learning (RL) framework that is able to explore environments without using any extrinsic reward and transfer effectively the learned skills to downstream tasks. We advance the state of the art in three ways. First, we propose a multiscale entropy optimization to take care of the fact that previous maximum state entropy, for lifelong exploration with millions of state observations, suffers from vanishing rewards and becomes very expensive computationally across iterations. Therefore, we add an episodic maximum entropy over each episode to speedup the search further. Second, we propose a novel intrinsic reward for episodic entropy maximization named \emph{average episodic state entropy} which provides the optimal solution for a theoretical upper bound of the episodic state entropy objective. Third, to speed the lifelong entropy maximization, we propose a $k$ nearest neighbors ($k$NN) graph to organize the estimation of the entropy and updating processes that reduces the computation substantially. Our ELEMENT significantly outperforms state-of-the-art intrinsic rewards in both episodic and lifelong setups. Moreover, it can be exploited in task-agnostic pre-training, collecting data for offline reinforcement learning, etc.

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arXiv2024

Cauchy-Schwarz Divergence Information Bottleneck for Regression

The information bottleneck (IB) approach is popular to improve the generalization, robustness and explainability of deep neural networks. Essentially, it aims to find a minimum sufficient representation $\mathbf{t}$ by striking a trade-off between a compression term $I(\mathbf{x};\mathbf{t})$ and a prediction term $I(y;\mathbf{t})$, where $I(\cdot;\cdot)$ refers to the mutual information (MI). MI is for the IB for the most part expressed in terms of the Kullback-Leibler (KL) divergence, which in the regression case corresponds to prediction based on mean squared error (MSE) loss with Gaussian assumption and compression approximated by variational inference. In this paper, we study the IB principle for the regression problem and develop a new way to parameterize the IB with deep neural networks by exploiting favorable properties of the Cauchy-Schwarz (CS) divergence. By doing so, we move away from MSE-based regression and ease estimation by avoiding variational approximations or distributional assumptions. We investigate the improved generalization ability of our proposed CS-IB and demonstrate strong adversarial robustness guarantees. We demonstrate its superior performance on six real-world regression tasks over other popular deep IB approaches. We additionally observe that the solutions discovered by CS-IB always achieve the best trade-off between prediction accuracy and compression ratio in the information plane. The code is available at \url{https://github.com/SJYuCNEL/Cauchy-Schwarz-Information-Bottleneck}.

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arXiv2024

The Normalized Cross Density Functional: A Framework to Quantify Statistical Dependence for Random Processes

This paper presents a novel approach to measuring statistical dependence between two random processes (r.p.) using a positive-definite function called the Normalized Cross Density (NCD). NCD is derived directly from the probability density functions of two r.p. and constructs a data-dependent Hilbert space, the Normalized Cross-Density Hilbert Space (NCD-HS). By Mercer's Theorem, the NCD norm can be decomposed into its eigenspectrum, which we name the Multivariate Statistical Dependence (MSD) measure, and their sum, the Total Dependence Measure (TSD). Hence, the NCD-HS eigenfunctions serve as a novel embedded feature space, suitable for quantifying r.p. statistical dependence. In order to apply NCD directly to r.p. realizations, we introduce an architecture with two multiple-output neural networks, a cost function, and an algorithm named the Functional Maximal Correlation Algorithm (FMCA). With FMCA, the two networks learn concurrently by approximating each other's outputs, extending the Alternating Conditional Expectation (ACE) for multivariate functions. We mathematically prove that FMCA learns the dominant eigenvalues and eigenfunctions of NCD directly from realizations. Preliminary results with synthetic data and medium-sized image datasets corroborate the theory. Different strategies for applying NCD are proposed and discussed, demonstrating the method's versatility and stability beyond supervised learning. Specifically, when the two r.p. are high-dimensional real-world images and a white uniform noise process, FMCA learns factorial codes, i.e., the occurrence of a code guarantees that a specific training set image was present, which is important for feature learning.

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arXiv2024

Weakly-Supervised Semantic Segmentation of Circular-Scan, Synthetic-Aperture-Sonar Imagery

We propose a weakly-supervised framework for the semantic segmentation of circular-scan synthetic-aperture-sonar (CSAS) imagery. The first part of our framework is trained in a supervised manner, on image-level labels, to uncover a set of semi-sparse, spatially-discriminative regions in each image. The classification uncertainty of each region is then evaluated. Those areas with the lowest uncertainties are then chosen to be weakly labeled segmentation seeds, at the pixel level, for the second part of the framework. Each of the seed extents are progressively resized according to an unsupervised, information-theoretic loss with structured-prediction regularizers. This reshaping process uses multi-scale, adaptively-weighted features to delineate class-specific transitions in local image content. Content-addressable memories are inserted at various parts of our framework so that it can leverage features from previously seen images to improve segmentation performance for related images. We evaluate our weakly-supervised framework using real-world CSAS imagery that contains over ten seafloor classes and ten target classes. We show that our framework performs comparably to nine fully-supervised deep networks. Our framework also outperforms eleven of the best weakly-supervised deep networks. We achieve state-of-the-art performance when pre-training on natural imagery. The average absolute performance gap to the next-best weakly-supervised network is well over ten percent for both natural imagery and sonar imagery. This gap is found to be statistically significant.

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arXiv2023

An Alternate View on Optimal Filtering in an RKHS

Kernel Adaptive Filtering (KAF) are mathematically principled methods which search for a function in a Reproducing Kernel Hilbert Space. While they work well for tasks such as time series prediction and system identification they are plagued by a linear relationship between number of training samples and model size, hampering their use on the very large data sets common in today's data saturated world. Previous methods try to solve this issue by sparsification. We describe a novel view of optimal filtering which may provide a route towards solutions in a RKHS which do not necessarily have this linear growth in model size. We do this by defining a RKHS in which the time structure of a stochastic process is still present. Using correntropy [11], an extension of the idea of a covariance function, we create a time based functional which describes some potentially nonlinear desired mapping function. This form of a solution may provide a fruitful line of research for creating more efficient representations of functionals in a RKHS, while theoretically providing computational complexity in the test set similar to Wiener solution.

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arXiv2023

Labels, Information, and Computation: Efficient Learning Using Sufficient Labels

In supervised learning, obtaining a large set of fully-labeled training data is expensive. We show that we do not always need full label information on every single training example to train a competent classifier. Specifically, inspired by the principle of sufficiency in statistics, we present a statistic (a summary) of the fully-labeled training set that captures almost all the relevant information for classification but at the same time is easier to obtain directly. We call this statistic "sufficiently-labeled data" and prove its sufficiency and efficiency for finding the optimal hidden representations, on which competent classifier heads can be trained using as few as a single randomly-chosen fully-labeled example per class. Sufficiently-labeled data can be obtained from annotators directly without collecting the fully-labeled data first. And we prove that it is easier to directly obtain sufficiently-labeled data than obtaining fully-labeled data. Furthermore, sufficiently-labeled data is naturally more secure since it stores relative, instead of absolute, information. Extensive experimental results are provided to support our theory.

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arXiv2022

Adapting the Exploration Rate for Value-of-Information-Based Reinforcement Learning

In this paper, we consider the problem of adjusting the exploration rate when using value-of-information-based exploration. We do this by converting the value-of-information optimization into a problem of finding equilibria of a flow for a changing exploration rate. We then develop an efficient path-following scheme for converging to these equilibria and hence uncovering optimal action-selection policies. Under this scheme, the exploration rate is automatically adapted according to the agent's experiences. Global convergence is theoretically assured. We first evaluate our exploration-rate adaptation on the Nintendo GameBoy games Centipede and Millipede. We demonstrate aspects of the search process, like that it yields a hierarchy of state abstractions. We also show that our approach returns better policies in fewer episodes than conventional search strategies relying on heuristic, annealing-based exploration-rate adjustments. We then illustrate that these trends hold for deep, value-of-information-based agents that learn to play ten simple games and over forty more complicated games for the Nintendo GameBoy system. Performance either near or well above the level of human play is observed.

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arXiv2022

The Functional Wiener Filter

This paper presents a close form solution in Reproducing Kernel Hilbert Space (RKHS) for the famed Wiener filter, which we called the functional Wiener filter(FWF). Instead of using the Wiener-Hopf factorization theory, here we define a new lagged RKHS that embeds signal statistics based on the correntropy function. In essence, we extend Parzen$'$s work on the autocorrelation function RKHS to nonlinear functional spaces. The FWF derivation is also quite different from kernel adaptive filtering (KAF) algorithms, which utilize a search approach. The analytic FWF solution is derived in the Gaussian kernel RKHS with a constant computational complexity similar to the Wiener solution, and never composes nor employs the error as in conventional optimal modeling. Because of the lack of congruence between the Gaussian RKHS and the space of time series, we compare performance of two pre-imaging algorithms: a fixed-point optimization (FWFFP) that finds and approximate solution in the RKHS, and a local model implementation named FWFLM. The experimental results show that the FWF performance is on par with the KAF for time series modeling, and it requires far less computation.

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arXiv2022

Quantifying Model Uncertainty for Semantic Segmentation using Operators in the RKHS

Deep learning models for semantic segmentation are prone to poor performance in real-world applications due to the highly challenging nature of the task. Model uncertainty quantification (UQ) is one way to address this issue of lack of model trustworthiness by enabling the practitioner to know how much to trust a segmentation output. Current UQ methods in this application domain are mainly restricted to Bayesian based methods which are computationally expensive and are only able to extract central moments of uncertainty thereby limiting the quality of their uncertainty estimates. We present a simple framework for high-resolution predictive uncertainty quantification of semantic segmentation models that leverages a multi-moment functional definition of uncertainty associated with the model's feature space in the reproducing kernel Hilbert space (RKHS). The multiple uncertainty functionals extracted from this framework are defined by the local density dynamics of the model's feature space and hence automatically align themselves at the tail-regions of the intrinsic probability density function of the feature space (where uncertainty is the highest) in such a way that the successively higher order moments quantify the more uncertain regions. This leads to a significantly more accurate view of model uncertainty than conventional Bayesian methods. Moreover, the extraction of such moments is done in a single-shot computation making it much faster than Bayesian and ensemble approaches (that involve a high number of forward stochastic passes of the model to quantify its uncertainty). We demonstrate these advantages through experimental evaluations of our framework implemented over four different state-of-the-art model architectures that are trained and evaluated on two benchmark road-scene segmentation datasets (Camvid and Cityscapes).

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arXiv2022

Robust Dependence Measure using RKHS based Uncertainty Moments and Optimal Transport

Reliable measurement of dependence between variables is essential in many applications of statistics and machine learning. Current approaches for dependence estimation, especially density-based approaches, lack in precision, robustness and/or interpretability (in terms of the type of dependence being estimated). We propose a two-step approach for dependence quantification between random variables: 1) We first decompose the probability density functions (PDF) of the variables involved in terms of multiple local moments of uncertainty that systematically and precisely identify the different regions of the PDF (with special emphasis on the tail-regions). 2) We then compute an optimal transport map to measure the geometric similarity between the corresponding sets of decomposed local uncertainty moments of the variables. Dependence is then determined by the degree of one-to-one correspondence between the respective uncertainty moments of the variables in the optimal transport map. We utilize a recently introduced Gaussian reproducing kernel Hilbert space (RKHS) based framework for multi-moment uncertainty decomposition of the variables. Being based on the Gaussian RKHS, our approach is robust towards outliers and monotone transformations of data, while the multiple moments of uncertainty provide high resolution and interpretability of the type of dependence being quantified. We support these claims through some preliminary results using simulated data.

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arXiv2022

Training Deep Architectures Without End-to-End Backpropagation: A Survey on the Provably Optimal Methods

This tutorial paper surveys provably optimal alternatives to end-to-end backpropagation (E2EBP) -- the de facto standard for training deep architectures. Modular training refers to strictly local training without both the forward and the backward pass, i.e., dividing a deep architecture into several nonoverlapping modules and training them separately without any end-to-end operation. Between the fully global E2EBP and the strictly local modular training, there are weakly modular hybrids performing training without the backward pass only. These alternatives can match or surpass the performance of E2EBP on challenging datasets such as ImageNet, and are gaining increasing attention primarily because they offer practical advantages over E2EBP, which will be enumerated herein. In particular, they allow for greater modularity and transparency in deep learning workflows, aligning deep learning with the mainstream computer science engineering that heavily exploits modularization for scalability. Modular training has also revealed novel insights about learning and has further implications on other important research domains. Specifically, it induces natural and effective solutions to some important practical problems such as data efficiency and transferability estimation.

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arXiv2022

Principle of Relevant Information for Graph Sparsification

Graph sparsification aims to reduce the number of edges of a graph while maintaining its structural properties. In this paper, we propose the first general and effective information-theoretic formulation of graph sparsification, by taking inspiration from the Principle of Relevant Information (PRI). To this end, we extend the PRI from a standard scalar random variable setting to structured data (i.e., graphs). Our Graph-PRI objective is achieved by operating on the graph Laplacian, made possible by expressing the graph Laplacian of a subgraph in terms of a sparse edge selection vector $\mathbf{w}$. We provide both theoretical and empirical justifications on the validity of our Graph-PRI approach. We also analyze its analytical solutions in a few special cases. We finally present three representative real-world applications, namely graph sparsification, graph regularized multi-task learning, and medical imaging-derived brain network classification, to demonstrate the effectiveness, the versatility and the enhanced interpretability of our approach over prevalent sparsification techniques. Code of Graph-PRI is available at https://github.com/SJYuCNEL/PRI-Graphs

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