A Likelihood Based Approach to Distribution Regression Using Conditional Deep Generative Models

In this work, we explore the theoretical properties of conditional deep generative models under the statistical framework of distribution regression where the response variable lies in a high-dimensional ambient space but concentrates around a potentially lower-dimensional manifold. More specifically, we study the large-sample properties of a likelihood-based approach for estimating these models. Our results lead to the convergence rate of a sieve maximum likelihood estimator (MLE) for estimating the conditional distribution (and its devolved counterpart) of the response given predictors in the Hellinger (Wasserstein) metric. Our rates depend solely on the intrinsic dimension and smoothness of the true conditional distribution. These findings provide an explanation of why conditional deep generative models can circumvent the curse of dimensionality from the perspective of statistical foundations and demonstrate that they can learn a broader class of nearly singular conditional distributions. Our analysis also emphasizes the importance of introducing a small noise perturbation to the data when they are supported sufficiently close to a manifold. Finally, in our numerical studies, we demonstrate the effective implementation of the proposed approach using both synthetic and real-world datasets, which also provide complementary validation to our theoretical findings.

Doubly Robust Conditional Independence Testing with Generative Neural Networks

This article addresses the problem of testing the conditional independence of two generic random vectors $X$ and $Y$ given a third random vector $Z$, which plays an important role in statistical and machine learning applications. We propose a new non-parametric testing procedure that avoids explicitly estimating any conditional distributions but instead requires sampling from the two marginal conditional distributions of $X$ given $Z$ and $Y$ given $Z$. We further propose using a generative neural network (GNN) framework to sample from these approximated marginal conditional distributions, which tends to mitigate the curse of dimensionality due to its adaptivity to any low-dimensional structures and smoothness underlying the data. Theoretically, our test statistic is shown to enjoy a doubly robust property against GNN approximation errors, meaning that the test statistic retains all desirable properties of the oracle test statistic utilizing the true marginal conditional distributions, as long as the product of the two approximation errors decays to zero faster than the parametric rate. Asymptotic properties of our statistic and the consistency of a bootstrap procedure are derived under both null and local alternatives. Extensive numerical experiments and real data analysis illustrate the effectiveness and broad applicability of our proposed test.

CHASE: A Causal Heterogeneous Graph based Framework for Root Cause Analysis in Multimodal Microservice Systems

In recent years, the widespread adoption of distributed microservice architectures within the industry has significantly increased the demand for enhanced system availability and robustness. Due to the complex service invocation paths and dependencies at enterprise-level microservice systems, it is challenging to locate the anomalies promptly during service invocations, thus causing intractable issues for normal system operations and maintenance. In this paper, we propose a Causal Heterogeneous grAph baSed framEwork for root cause analysis, namely CHASE, for microservice systems with multimodal data, including traces, logs, and system monitoring metrics. Specifically, related information is encoded into representative embeddings and further modeled by a multimodal invocation graph. Following that, anomaly detection is performed on each instance node with attentive heterogeneous message passing from its adjacent metric and log nodes. Finally, CHASE learns from the constructed hypergraph with hyperedges representing the flow of causality and performs root cause localization. We evaluate the proposed framework on two public microservice datasets with distinct attributes and compare with the state-of-the-art methods. The results show that CHASE achieves the average performance gain up to 36.2%(A@1) and 29.4%(Percentage@1), respectively to its best counterpart.

TF4CTR: Twin Focus Framework for CTR Prediction via Adaptive Sample Differentiation

Effective feature interaction modeling is critical for enhancing the accuracy of click-through rate (CTR) prediction in industrial recommender systems. Most of the current deep CTR models resort to building complex network architectures to better capture intricate feature interactions or user behaviors. However, we identify two limitations in these models: (1) the samples given to the model are undifferentiated, which may lead the model to learn a larger number of easy samples in a single-minded manner while ignoring a smaller number of hard samples, thus reducing the model's generalization ability; (2) differentiated feature interaction encoders are designed to capture different interactions information but receive consistent supervision signals, thereby limiting the effectiveness of the encoder. To bridge the identified gaps, this paper introduces a novel CTR prediction framework by integrating the plug-and-play Twin Focus (TF) Loss, Sample Selection Embedding Module (SSEM), and Dynamic Fusion Module (DFM), named the Twin Focus Framework for CTR (TF4CTR). Specifically, the framework employs the SSEM at the bottom of the model to differentiate between samples, thereby assigning a more suitable encoder for each sample. Meanwhile, the TF Loss provides tailored supervision signals to both simple and complex encoders. Moreover, the DFM dynamically fuses the feature interaction information captured by the encoders, resulting in more accurate predictions. Experiments on five real-world datasets confirm the effectiveness and compatibility of the framework, demonstrating its capacity to enhance various representative baselines in a model-agnostic manner. To facilitate reproducible research, our open-sourced code and detailed running logs will be made available at: https://github.com/salmon1802/TF4CTR.

A Practical Beamforming Design for Active RIS-assisted MU-MISO Systems

Reconfigurable Intelligent Surfaces (RIS) have been proposed as a revolutionary technology with the potential to address several critical requirements of 6G communication systems. Despite its powerful ability for radio environment reconfiguration, the ``double fading'' effect constricts the practical system performance enhancements due to the significant path loss. A new active RIS architecture has been recently proposed to overcome this challenge. However, existing active RIS studies rely on an ideal amplification model without considering the practical hardware limitation of amplifiers, which may cause performance degradation using such inaccurate active RIS modeling. Motivated by this fact, in this paper we first investigate the amplification principle of typical active RIS and propose a more accurate amplification model based on amplifier hardware characteristics. Then, based on the new amplification model, we propose a novel joint transmit beamforming and RIS reflection beamforming design considering the incident signal power on practical active RIS for multiuser multi-input single-output (MU-MISO) communication system. Fractional programming (FP), majorization minimization (MM) and block coordinate descent (BCD) methods are used to solve for the complex problem. Simulation results indicate the importance of the consideration of practical amplifier hardware characteristics in the joint beamforming designs and demonstrate the effectiveness of the proposed algorithm compared to other benchmarks.

Bayesian Model Selection via Mean-Field Variational Approximation

This article considers Bayesian model selection via mean-field (MF) variational approximation. Towards this goal, we study the non-asymptotic properties of MF inference under the Bayesian framework that allows latent variables and model mis-specification. Concretely, we show a Bernstein von-Mises (BvM) theorem for the variational distribution from MF under possible model mis-specification, which implies the distributional convergence of MF variational approximation to a normal distribution centering at the maximal likelihood estimator (within the specified model). Motivated by the BvM theorem, we propose a model selection criterion using the evidence lower bound (ELBO), and demonstrate that the model selected by ELBO tends to asymptotically agree with the one selected by the commonly used Bayesian information criterion (BIC) as sample size tends to infinity. Comparing to BIC, ELBO tends to incur smaller approximation error to the log-marginal likelihood (a.k.a. model evidence) due to a better dimension dependence and full incorporation of the prior information. Moreover, we show the geometric convergence of the coordinate ascent variational inference (CAVI) algorithm under the parametric model framework, which provides a practical guidance on how many iterations one typically needs to run when approximating the ELBO. These findings demonstrate that variational inference is capable of providing a computationally efficient alternative to conventional approaches in tasks beyond obtaining point estimates, which is also empirically demonstrated by our extensive numerical experiments.

A Gromov--Wasserstein Geometric View of Spectrum-Preserving Graph Coarsening

Graph coarsening is a technique for solving large-scale graph problems by working on a smaller version of the original graph, and possibly interpolating the results back to the original graph. It has a long history in scientific computing and has recently gained popularity in machine learning, particularly in methods that preserve the graph spectrum. This work studies graph coarsening from a different perspective, developing a theory for preserving graph distances and proposing a method to achieve this. The geometric approach is useful when working with a collection of graphs, such as in graph classification and regression. In this study, we consider a graph as an element on a metric space equipped with the Gromov--Wasserstein (GW) distance, and bound the difference between the distance of two graphs and their coarsened versions. Minimizing this difference can be done using the popular weighted kernel $K$-means method, which improves existing spectrum-preserving methods with the proper choice of the kernel. The study includes a set of experiments to support the theory and method, including approximating the GW distance, preserving the graph spectrum, classifying graphs using spectral information, and performing regression using graph convolutional networks. Code is available at https://github.com/ychen-stat-ml/GW-Graph-Coarsening .

On the Convergence of Coordinate Ascent Variational Inference

As a computational alternative to Markov chain Monte Carlo approaches, variational inference (VI) is becoming more and more popular for approximating intractable posterior distributions in large-scale Bayesian models due to its comparable efficacy and superior efficiency. Several recent works provide theoretical justifications of VI by proving its statistical optimality for parameter estimation under various settings; meanwhile, formal analysis on the algorithmic convergence aspects of VI is still largely lacking. In this paper, we consider the common coordinate ascent variational inference (CAVI) algorithm for implementing the mean-field (MF) VI towards optimizing a Kullback--Leibler divergence objective functional over the space of all factorized distributions. Focusing on the two-block case, we analyze the convergence of CAVI by leveraging the extensive toolbox from functional analysis and optimization. We provide general conditions for certifying global or local exponential convergence of CAVI. Specifically, a new notion of generalized correlation for characterizing the interaction between the constituting blocks in influencing the VI objective functional is introduced, which according to the theory, quantifies the algorithmic contraction rate of two-block CAVI. As illustrations, we apply the developed theory to a number of examples, and derive explicit problem-dependent upper bounds on the algorithmic contraction rate.

CTSN: Predicting Cloth Deformation for Skeleton-based Characters with a Two-stream Skinning Network

We present a novel learning method to predict the cloth deformation for skeleton-based characters with a two-stream network. The characters processed in our approach are not limited to humans, and can be other skeletal-based representations of non-human targets such as fish or pets. We use a novel network architecture which consists of skeleton-based and mesh-based residual networks to learn the coarse and wrinkle features as the overall residual from the template cloth mesh. Our network is used to predict the deformation for loose or tight-fitting clothing or dresses. We ensure that the memory footprint of our network is low, and thereby result in reduced storage and computational requirements. In practice, our prediction for a single cloth mesh for the skeleton-based character takes about 7 milliseconds on an NVIDIA GeForce RTX 3090 GPU. Compared with prior methods, our network can generate fine deformation results with details and wrinkles.

Statistically Optimal K-means Clustering via Nonnegative Low-rank Semidefinite Programming

$K$-means clustering is a widely used machine learning method for identifying patterns in large datasets. Semidefinite programming (SDP) relaxations have recently been proposed for solving the $K$-means optimization problem that enjoy strong statistical optimality guarantees, but the prohibitive cost of implementing an SDP solver renders these guarantees inaccessible to practical datasets. By contrast, nonnegative matrix factorization (NMF) is a simple clustering algorithm that is widely used by machine learning practitioners, but without a solid statistical underpinning nor rigorous guarantees. In this paper, we describe an NMF-like algorithm that works by solving a nonnegative low-rank restriction of the SDP relaxed $K$-means formulation using a nonconvex Burer--Monteiro factorization approach. The resulting algorithm is just as simple and scalable as state-of-the-art NMF algorithms, while also enjoying the same strong statistical optimality guarantees as the SDP. In our experiments, we observe that our algorithm achieves substantially smaller mis-clustering errors compared to the existing state-of-the-art.