arXiv subjects

Fan Bu

Publications and source records attributed to Fan Bu.

35 records · Page 2Linked to original sources

arXiv2025

Besov--Triebel--Lizorkin-Type Spaces with Matrix $A_\infty$ Weights

Introduced by A. Volberg, matrix $A_{p,\infty}$ weights provide a suitable generalization of Muckenhoupt $A_\infty$ weights from the classical theory. In our previous work, we established new characterizations of these weights. Here, we use these results to study inhomogeneous Besov-type and Triebel--Lizorkin-type spaces with such weights. In particular, we characterize these spaces, in terms of the $φ$-transform, molecules, and wavelets, and obtain the boundedness of almost diagonal operators, pseudo-differential operators, trace operators, pointwise multipliers, and Calderón--Zygmund operators on these spaces. This is the first systematic study of inhomogeneous Besov--Triebel--Lizorkin-type spaces with $A_{p,\infty}$-matrix weights, but some of the results are new even when specialized to the scalar unweighted case.

math.FA↗

arXiv2024

Roadmap towards Superhuman Speech Understanding using Large Language Models

The success of large language models (LLMs) has prompted efforts to integrate speech and audio data, aiming to create general foundation models capable of processing both textual and non-textual inputs. Recent advances, such as GPT-4o, highlight the potential for end-to-end speech LLMs, which preserves non-semantic information and world knowledge for deeper speech understanding. To guide the development of speech LLMs, we propose a five-level roadmap, ranging from basic automatic speech recognition (ASR) to advanced superhuman models capable of integrating non-semantic information with abstract acoustic knowledge for complex tasks. Moreover, we design a benchmark, SAGI Bechmark, that standardizes critical aspects across various tasks in these five levels, uncovering challenges in using abstract acoustic knowledge and completeness of capability. Our findings reveal gaps in handling paralinguistic cues and abstract acoustic knowledge, and we offer future directions. This paper outlines a roadmap for advancing speech LLMs, introduces a benchmark for evaluation, and provides key insights into their current limitations and potential.

cs.CL↗

arXiv2024

Matrix-Weighted Besov-Type and Triebel--Lizorkin-Type Spaces II: Sharp Boundedness of Almost Diagonal Operators

This article is the second one of three successive articles of the authors on the matrix-weighted Besov-type and Triebel--Lizorkin-type spaces. In this article, we obtain the sharp boundedness of almost diagonal operators on matrix-weighted Besov-type and Triebel--Lizorkin-type sequence spaces. These results not only possess broad generality but also improve several existing related results in various special cases covered by this family of spaces. This improvement depends, on the one hand, on the notion of $A_p$-dimensions of matrix weights and their properties introduced in the first article of this series and, on the other hand, on a careful direct analysis of sequences of averages avoiding maximal operators. While a recent matrix-weighted extension of the Fefferman--Stein vector-valued maximal inequality would provide an alternative route to some of our results in the restricted range of function space parameters $p,q\in(1,\infty)$, our approach covers the full scale of exponents $p\in(0,\infty)$ and $q\in(0,\infty]$ that is relevant in the theory of function spaces.

math.FA↗

arXiv2024

CM-TTS: Enhancing Real Time Text-to-Speech Synthesis Efficiency through Weighted Samplers and Consistency Models

Neural Text-to-Speech (TTS) systems find broad applications in voice assistants, e-learning, and audiobook creation. The pursuit of modern models, like Diffusion Models (DMs), holds promise for achieving high-fidelity, real-time speech synthesis. Yet, the efficiency of multi-step sampling in Diffusion Models presents challenges. Efforts have been made to integrate GANs with DMs, speeding up inference by approximating denoising distributions, but this introduces issues with model convergence due to adversarial training. To overcome this, we introduce CM-TTS, a novel architecture grounded in consistency models (CMs). Drawing inspiration from continuous-time diffusion models, CM-TTS achieves top-quality speech synthesis in fewer steps without adversarial training or pre-trained model dependencies. We further design weighted samplers to incorporate different sampling positions into model training with dynamic probabilities, ensuring unbiased learning throughout the entire training process. We present a real-time mel-spectrogram generation consistency model, validated through comprehensive evaluations. Experimental results underscore CM-TTS's superiority over existing single-step speech synthesis systems, representing a significant advancement in the field.

cs.SD↗

arXiv2023

Matrix-Weighted Besov-Type and Triebel--Lizorkin-Type Spaces III: Characterizations of Molecules and Wavelets, Trace Theorems, and Boundedness of Pseudo-Differential Operators and Calderón--Zygmund Operators

This is the last one of three successive articles by the authors on matrix-weighted Besov-type and Triebel--Lizorkin-type spaces $\dot B^{s,τ}_{p,q}(W)$ and $\dot F^{s,τ}_{p,q}(W)$. In this article, the authors establish the molecular and the wavelet characterizations of these spaces. Furthermore, as applications, the authors obtain the optimal boundedness of trace operators, pseudo-differential operators, and Calderón--Zygmund operators on these spaces. Due to the sharp boundedness of almost diagonal operators on their related sequence spaces obtained in the second article of this series, all results presented in this article improve their counterparts on matrix-weighted Besov and Triebel--Lizorkin spaces $\dot B^{s}_{p,q}(W)$ and $\dot F^{s}_{p,q}(W)$. In particular, even when reverting to the boundedness of Calderón--Zygmund operator on unweighted Triebel--Lizorkin spaces $\dot F^{s}_{p,q}$, these results are still better.

math.FA↗

arXiv2023

Matrix-Weighted Besov-Type and Triebel--Lizorkin-Type Spaces I: $A_p$-Dimensions of Matrix Weights and $φ$-Transform Characterizations

Let $s\in{\mathbb R}$, $q\in (0,\infty]$, and $τ\in[0,\infty)$. It is well known that Besov-type spaces $\dot B^{s,τ}_{p,q}$ with $p\in (0,\infty]$ and Triebel--Lizorkin-type spaces $\dot F^{s,τ}_{p,q}$ with $p\in (0,\infty)$ when $τ\in [0,\infty)$ or with $p\in (0,\infty]$ when $τ=0$ on $\mathbb{R}^n$ consist of a general family of function spaces that cover not only the well-known Besov and Triebel--Lizorkin spaces $\dot B^{s}_{p,q}$ and $\dot F^{s}_{p,q}$ (when $τ=0$) but also several other function spaces of interest, such as Morrey spaces and $Q$ spaces. In three successive articles, the authors develop a complete real-variable theory of matrix-weighted Besov-type spaces $\dot B^{s,τ}_{p,q}(W)$ and matrix-weighted Triebel--Lizorkin-type spaces $\dot F^{s,τ}_{p,q}(W)$ on $\mathbb{R}^n$, where $W$ is a matrix-valued Muckenhoupt $A_p$ weight. This article is the first one, whose main novelty exists in that the authors introduce the new concept, $A_p$-dimensions of matrix weights, and intensively study their properties, especially those elaborate properties expressed via reducing operators. The authors then introduce the spaces $\dot B^{s,τ}_{p,q}(W)$ and $\dot F^{s,τ}_{p,q}(W)$ and, using $A_p$-dimensions and their nice properties, the authors establish the $φ$-transform characterization of $\dot B^{s,τ}_{p,q}(W)$ and $\dot F^{s,τ}_{p,q}(W)$. The $A_p$-dimensions of matrix weights and their properties also enable the authors to obtain the sharp boundedness of almost diagonal operators on related sequence spaces in the subsequent second article and the optimal characterizations of molecules and wavelets, trace theorems, and the optimal boundedness of pseudo-differential operators and Calderón--Zygmund operators in the subsequent third article.

math.FA↗

arXiv2023

New Characterizations and Properties of Matrix $A_\infty$ Weights

We provide several new characterizations of $A_{p,\infty}$-matrix weights, originally introduced by A. Volberg as matrix-valued substitutes of the classical $A_\infty$ weights. In analogy with the notion of $A_p$-dimension of matrix weights introduced in our previous work, we introduce the concepts of the lower and the upper dimensions of $A_{p,\infty}$-matrix weights, which enable us to obtain sharp estimates related to their reducing operators. In a follow-up work, these results will play a key role in the study of function spaces with $A_{p,\infty}$-matrix weights, which extends earlier results in the more restricted class of $A_p$-matrix weights.

math.FA↗

arXiv2023

Bayesian Safety Surveillance with Adaptive Bias Correction

Post-market safety surveillance is an integral part of mass vaccination programs. Typically relying on sequential analysis of real-world health data as they accrue, safety surveillance is challenged by the difficulty of sequential multiple testing and by biases induced by residual confounding. The current standard approach based on the maximized sequential probability ratio test (MaxSPRT) fails to satisfactorily address these practical challenges and it remains a rigid framework that requires pre-specification of the surveillance schedule. We develop an alternative Bayesian surveillance procedure that addresses both challenges using a more flexible framework. We adopt a joint statistical modeling approach to sequentially estimate the effect of vaccine exposure on the adverse event of interest and correct for estimation bias by simultaneously analyzing a large set of negative control outcomes through a Bayesian hierarchical model. We then compute a posterior probability of the alternative hypothesis via Markov chain Monte Carlo sampling and use it for sequential detection of safety signals. Through an empirical evaluation using six US observational healthcare databases covering more than 360 million patients, we benchmark the proposed procedure against MaxSPRT on testing errors and estimation accuracy, under two epidemiological designs, the historical comparator and the self-controlled case series. We demonstrate that our procedure substantially reduces Type 1 error rates, maintains high statistical power, delivers fast signal detection, and provides considerably more accurate estimation. As an effort to promote open science, we present all empirical results in an R ShinyApp and provide full implementation of our method in the R package EvidenceSynthesis.

stat.ME↗

arXiv2023

Inferring HIV Transmission Patterns from Viral Deep-Sequence Data via Latent Typed Point Processes

Viral deep-sequencing data play a crucial role toward understanding disease transmission network flows, because the higher resolution of these data compared to standard Sanger sequencing provide evidence into the direction of infectious disease transmission. To more fully utilize these rich data and account for the uncertainties in phylogenetic analysis outcomes, we propose a spatial Poisson process model to uncover HIV transmission flow patterns at the population level. We represent pairings of two individuals with viral sequence data as typed points, with coordinates representing covariates such as gender and age, and the point type representing the unobserved transmission statuses (linkage and direction). Points are associated with observed scores on the strength of evidence for each transmission status that are obtained through standard deep-sequenece phylogenetic analysis. Our method is able to jointly infer the latent transmission statuses for all pairings and the transmission flow surface on the source-recipient covariate space. In contrast to existing methods, our framework does not require pre-classification of the transmission statuses of data points, instead learning them probabilistically through a fully Bayesian inference scheme. By directly modeling continuous spatial processes with smooth densities, our method enjoys significant computational advantages compared to previous methods that rely on discretization of the covariate space. We demonstrate that our framework can capture age structures in HIV transmission at high resolution, and bring valuable insights in a case study on viral deep-sequencing data from Southern Uganda.

stat.ME↗

arXiv2022

Adjusting for both sequential testing and systematic error in safety surveillance using observational data: Empirical calibration and MaxSPRT

Post-approval safety surveillance of medical products using observational healthcare data can help identify safety issues beyond those found in pre-approval trials. When testing sequentially as data accrue, maximum sequential probability ratio testing (MaxSPRT) is a common approach to maintaining nominal type 1 error. However, the true type 1 error may still deviate from the specified one because of systematic error due to the observational nature of the analysis. This systematic error may persist even after controlling for known confounders. Here we propose to address this issue by combing MaxSPRT with empirical calibration. In empirical calibration, we assume uncertainty about the systematic error in our analysis, the source of uncertainty commonly overlooked in practice. We infer a probability distribution of systematic error by relying on a large set of negative controls: exposure-outcome where no causal effect is believed to exist. Integrating this distribution into our test statistics has previously been shown to restore type 1 error to nominal. Here we show how we can calibrate the critical value central to MaxSPRT. We evaluate this novel approach using simulations and real electronic health records, using H1N1 vaccinations during the 2009-2010 season as an example. Results show that combining empirical calibration with MaxSPRT restores nominal type 1 error. In our real-world example, adjusting for systematic error using empirical calibration has a larger impact than, and hence is just as essential as, adjusting for sequential testing using MaxSPRT. We recommend performing both, using the method described here.

stat.ME↗

arXiv2021

Likelihood-based inference for partially observed stochastic epidemics with individual heterogeneity

We develop a stochastic epidemic model progressing over dynamic networks, where infection rates are heterogeneous and may vary with individual-level covariates. The joint dynamics are modeled as a continuous-time Markov chain such that disease transmission is constrained by the contact network structure, and network evolution is in turn influenced by individual disease statuses. To accommodate partial epidemic observations commonly seen in real-world data, we propose a likelihood-based inference method based on the stochastic EM algorithm, introducing key innovations that include efficient conditional samplers for imputing missing infection and recovery times which respect the dynamic contact network. Experiments on both synthetic and real datasets demonstrate that our inference method can accurately and efficiently recover model parameters and provide valuable insight at the presence of unobserved disease episodes in epidemic data.

stat.ME↗

arXiv2020

Bridging the Gap Between Safety and Real-Time Performance in Receding-Horizon Trajectory Design for Mobile Robots

To operate with limited sensor horizons in unpredictable environments, autonomous robots use a receding-horizon strategy to plan trajectories, wherein they execute a short plan while creating the next plan. However, creating safe, dynamically-feasible trajectories in real time is challenging; and, planners must ensure persistent feasibility, meaning a new trajectory is always available before the previous one has finished executing. Existing approaches make a tradeoff between model complexity and planning speed, which can require sacrificing guarantees of safety and dynamic feasibility. This work presents the Reachability-based Trajectory Design (RTD) method for trajectory planning. RTD begins with an offline Forward Reachable Set (FRS) computation of a robot's motion when tracking parameterized trajectories; the FRS provably bounds tracking error. At runtime, the FRS is used to map obstacles to parameterized trajectories, allowing RTD to select a safe trajectory at every planning iteration. RTD prescribes an obstacle representation to ensure that obstacle constraints can be created and evaluated in real time while maintaining safety. Persistent feasibility is achieved by prescribing a minimum sensor horizon and a minimum duration for the planned trajectories. A system decomposition approach is used to improve the tractability of computing the FRS, allowing RTD to create more complex plans at runtime. RTD is compared in simulation with Rapidly-Exploring Random Trees and Nonlinear Model-Predictive Control. RTD is also demonstrated in randomly-crafted environments on two hardware platforms: a differential-drive Segway, and a car-like Rover. The proposed method is safe and persistently feasible across thousands of simulations and dozens of real-world hardware demos.

cs.RO↗

arXiv2020

Likelihood-based Inference for Partially Observed Epidemics on Dynamic Networks

We propose a generative model and an inference scheme for epidemic processes on dynamic, adaptive contact networks. Network evolution is formulated as a link-Markovian process, which is then coupled to an individual-level stochastic SIR model, in order to describe the interplay between epidemic dynamics on a network and network link changes. A Markov chain Monte Carlo framework is developed for likelihood-based inference from partial epidemic observations, with a novel data augmentation algorithm specifically designed to deal with missing individual recovery times under the dynamic network setting. Through a series of simulation experiments, we demonstrate the validity and flexibility of the model as well as the efficacy and efficiency of the data augmentation inference scheme. The model is also applied to a recent real-world dataset on influenza-like-illness transmission with high-resolution social contact tracking records.

stat.ME↗

arXiv2019

Who Started It? Identifying Root Sources in Textual Conversation Threads

In textual conversation threads, as found on many popular social media platforms, each particular user text comment either originates a new thread of discussion, or replies to a previous comment. An individual who makes an original comment ---termed as the "root source''---is a topic initiator or even an information source, and identifying such individuals is of particular interest. The reply structure of comments is not always available (e.g. in the proliferation of a news event), and thus identifying root sources is a nontrivial task. In this paper, we develop a generative model based on marked multivariate Hawkes processes, and introduce a novel concept, "root source probability", to quantify the uncertainty in attributing possible root sources to each comment. A dynamic-programming-based algorithm is then derived to efficiently compute root source probabilities. Experiments on synthetic and real-world data show that our method identifies root sources that match ground truth and human intuition.

cs.SI↗

arXiv2019

Towards Provably Not-at-Fault Control of Autonomous Robots in Arbitrary Dynamic Environments

As autonomous robots increasingly become part of daily life, they will often encounter dynamic environments while only having limited information about their surroundings. Unfortunately, due to the possible presence of malicious dynamic actors, it is infeasible to develop an algorithm that can guarantee collision-free operation. Instead, one can attempt to design a control technique that guarantees the robot is not-at-fault in any collision. In the literature, making such guarantees in real time has been restricted to static environments or specific dynamic models. To ensure not-at-fault behavior, a robot must first correctly sense and predict the world around it within some sufficiently large sensor horizon (the prediction problem), then correctly control relative to the predictions (the control problem). This paper addresses the control problem by proposing Reachability-based Trajectory Design for Dynamic environments (RTD-D), which guarantees that a robot with an arbitrary nonlinear dynamic model correctly responds to predictions in arbitrary dynamic environments. RTD-D first computes a Forward Reachable Set (FRS) offline of the robot tracking parameterized desired trajectories that include fail-safe maneuvers. Then, for online receding-horizon planning, the method provides a way to discretize predictions of an arbitrary dynamic environment to enable real-time collision checking. The FRS is used to map these discretized predictions to trajectories that the robot can track while provably not-at-fault. One such trajectory is chosen at each iteration, or the robot executes the fail-safe maneuver from its previous trajectory which is guaranteed to be not at fault. RTD-D is shown to produce not-at-fault behavior over thousands of simulations and several real-world hardware demonstrations on two robots: a Segway, and a small electric vehicle.

cs.RO↗

arXiv2018

SMOGS: Social Network Metrics of Game Success

This paper develops metrics from a social network perspective that are directly translatable to the outcome of a basketball game. We extend a state-of-the-art multi-resolution stochastic process approach to modeling basketball by modeling passes between teammates as directed dynamic relational links on a network and introduce multiplicative latent factors to study higher-order patterns in players' interactions that distinguish a successful game from a loss. Parameters are estimated using a Markov chain Monte Carlo sampler. Results in simulation experiments suggest that the sampling scheme is effective in recovering the parameters. We then apply the model to the first high-resolution optical tracking dataset collected in college basketball games. The learned latent factors demonstrate significant differences between players' passing and receiving tendencies in a loss than those in a win. The model is applicable to team sports other than basketball, as well as other time-varying network observations.

stat.AP↗

arXiv2018

The Evolution of Popularity and Images of Characters in Marvel Cinematic Universe Fanfictions

This analysis proposes a new topic model to study the yearly trends in Marvel Cinematic Universe fanfictions on three levels: character popularity, character images/topics, and vocabulary pattern of topics. It is found that character appearances in fanfictions have become more diverse over the years thanks to constant introduction of new characters in feature films, and in the case of Captain America, multi-dimensional character development is well-received by the fanfiction world.

cs.CL↗