Large Deviation Analysis of Score-based Hypothesis Testing

Score-based statistical models play an important role in modern machine learning, statistics, and signal processing. For hypothesis testing, a score-based hypothesis test is proposed in \cite{wu2022score}. We analyze the performance of this score-based hypothesis testing procedure and derive upper bounds on the probabilities of its Type I and II errors. We prove that the exponents of our error bounds are asymptotically (in the number of samples) tight for the case of simple null and alternative hypotheses. We calculate these error exponents explicitly in specific cases and provide numerical studies for various other scenarios of interest.

Robust Quickest Change Detection for Unnormalized Models

Detecting an abrupt and persistent change in the underlying distribution of online data streams is an important problem in many applications. This paper proposes a new robust score-based algorithm called RSCUSUM, which can be applied to unnormalized models and addresses the issue of unknown post-change distributions. RSCUSUM replaces the Kullback-Leibler divergence with the Fisher divergence between pre- and post-change distributions for computational efficiency in unnormalized statistical models and introduces a notion of the ``least favorable'' distribution for robust change detection. The algorithm and its theoretical analysis are demonstrated through simulation studies.

Semi-Supervised Federated Learning for Keyword Spotting

Keyword Spotting (KWS) is a critical aspect of audio-based applications on mobile devices and virtual assistants. Recent developments in Federated Learning (FL) have significantly expanded the ability to train machine learning models by utilizing the computational and private data resources of numerous distributed devices. However, existing FL methods typically require that devices possess accurate ground-truth labels, which can be both expensive and impractical when dealing with local audio data. In this study, we first demonstrate the effectiveness of Semi-Supervised Federated Learning (SSL) and FL for KWS. We then extend our investigation to Semi-Supervised Federated Learning (SSFL) for KWS, where devices possess completely unlabeled data, while the server has access to a small amount of labeled data. We perform numerical analyses using state-of-the-art SSL, FL, and SSFL techniques to demonstrate that the performance of KWS models can be significantly improved by leveraging the abundant unlabeled heterogeneous data available on devices.

Pruning Deep Neural Networks from a Sparsity Perspective

In recent years, deep network pruning has attracted significant attention in order to enable the rapid deployment of AI into small devices with computation and memory constraints. Pruning is often achieved by dropping redundant weights, neurons, or layers of a deep network while attempting to retain a comparable test performance. Many deep pruning algorithms have been proposed with impressive empirical success. However, existing approaches lack a quantifiable measure to estimate the compressibility of a sub-network during each pruning iteration and thus may under-prune or over-prune the model. In this work, we propose PQ Index (PQI) to measure the potential compressibility of deep neural networks and use this to develop a Sparsity-informed Adaptive Pruning (SAP) algorithm. Our extensive experiments corroborate the hypothesis that for a generic pruning procedure, PQI decreases first when a large model is being effectively regularized and then increases when its compressibility reaches a limit that appears to correspond to the beginning of underfitting. Subsequently, PQI decreases again when the model collapse and significant deterioration in the performance of the model start to occur. Additionally, our experiments demonstrate that the proposed adaptive pruning algorithm with proper choice of hyper-parameters is superior to the iterative pruning algorithms such as the lottery ticket-based pruning methods, in terms of both compression efficiency and robustness.

Quickest Change Detection for Unnormalized Statistical Models

Classical quickest change detection algorithms require modeling pre-change and post-change distributions. Such an approach may not be feasible for various machine learning models because of the complexity of computing the explicit distributions. Additionally, these methods may suffer from a lack of robustness to model mismatch and noise. This paper develops a new variant of the classical Cumulative Sum (CUSUM) algorithm for the quickest change detection. This variant is based on Fisher divergence and the Hyv\"arinen score and is called the Score-based CUSUM (SCUSUM) algorithm. The SCUSUM algorithm allows the applications of change detection for unnormalized statistical models, i.e., models for which the probability density function contains an unknown normalization constant. The asymptotic optimality of the proposed algorithm is investigated by deriving expressions for average detection delay and the mean running time to a false alarm. Numerical results are provided to demonstrate the performance of the proposed algorithm.

Personalized Federated Recommender Systems with Private and Partially Federated AutoEncoders

Recommender Systems (RSs) have become increasingly important in many application domains, such as digital marketing. Conventional RSs often need to collect users' data, centralize them on the server-side, and form a global model to generate reliable recommendations. However, they suffer from two critical limitations: the personalization problem that the RSs trained traditionally may not be customized for individual users, and the privacy problem that directly sharing user data is not encouraged. We propose Personalized Federated Recommender Systems (PersonalFR), which introduces a personalized autoencoder-based recommendation model with Federated Learning (FL) to address these challenges. PersonalFR guarantees that each user can learn a personal model from the local dataset and other participating users' data without sharing local data, data embeddings, or models. PersonalFR consists of three main components, including AutoEncoder-based RSs (ARSs) that learn the user-item interactions, Partially Federated Learning (PFL) that updates the encoder locally and aggregates the decoder on the server-side, and Partial Compression (PC) that only computes and transmits active model parameters. Extensive experiments on two real-world datasets demonstrate that PersonalFR can achieve private and personalized performance comparable to that trained by centralizing all users' data. Moreover, PersonalFR requires significantly less computation and communication overhead than standard FL baselines.

A Theoretical Understanding of Neural Network Compression from Sparse Linear Approximation

The goal of model compression is to reduce the size of a large neural network while retaining a comparable performance. As a result, computation and memory costs in resource-limited applications may be significantly reduced by dropping redundant weights, neurons, or layers. There have been many model compression algorithms proposed that provide impressive empirical success. However, a theoretical understanding of model compression is still limited. One problem is understanding if a network is more compressible than another of the same structure. Another problem is quantifying how much one can prune a network with theoretically guaranteed accuracy degradation. In this work, we propose to use the sparsity-sensitive $\ell_q$-norm ($0<q<1$) to characterize compressibility and provide a relationship between soft sparsity of the weights in the network and the degree of compression with a controlled accuracy degradation bound. We also develop adaptive algorithms for pruning each neuron in the network informed by our theory. Numerical studies demonstrate the promising performance of the proposed methods compared with standard pruning algorithms.

A Physics-Informed Vector Quantized Autoencoder for Data Compression of Turbulent Flow

Analyzing large-scale data from simulations of turbulent flows is memory intensive, requiring significant resources. This major challenge highlights the need for data compression techniques. In this study, we apply a physics-informed Deep Learning technique based on vector quantization to generate a discrete, low-dimensional representation of data from simulations of three-dimensional turbulent flows. The deep learning framework is composed of convolutional layers and incorporates physical constraints on the flow, such as preserving incompressibility and global statistical characteristics of the velocity gradients. The accuracy of the model is assessed using statistical, comparison-based similarity and physics-based metrics. The training data set is produced from Direct Numerical Simulation of an incompressible, statistically stationary, isotropic turbulent flow. The performance of this lossy data compression scheme is evaluated not only with unseen data from the stationary, isotropic turbulent flow, but also with data from decaying isotropic turbulence, and a Taylor-Green vortex flow. Defining the compression ratio (CR) as the ratio of original data size to the compressed one, the results show that our model based on vector quantization can offer CR $=85$ with a mean square error (MSE) of $O(10^{-3})$, and predictions that faithfully reproduce the statistics of the flow, except at the very smallest scales where there is some loss. Compared to the recent study based on a conventional autoencoder where compression is performed in a continuous space, our model improves the CR by more than $30$ percent, and reduces the MSE by an order of magnitude. Our compression model is an attractive solution for situations where fast, high quality and low-overhead encoding and decoding of large data are required.