A key task for speech recognition systems is to reduce the mismatch between training and evaluation data that is often attributable to speaker differences. Speaker adaptation techniques play a vital role to reduce the mismatch. Model-based speaker adaptation approaches often require sufficient amounts of target speaker data to ensure robustness. When the amount of speaker level data is limited, speaker adaptation is prone to overfitting and poor generalization. To address the issue, this paper proposes a full Bayesian learning based DNN speaker adaptation framework to model speaker-dependent (SD) parameter uncertainty given limited speaker specific adaptation data. This framework is investigated in three forms of model based DNN adaptation techniques: Bayesian learning of hidden unit contributions (BLHUC), Bayesian parameterized activation functions (BPAct), and Bayesian hidden unit bias vectors (BHUB). In the three methods, deterministic SD parameters are replaced by latent variable posterior distributions for each speaker, whose parameters are efficiently estimated using a variational inference based approach. Experiments conducted on 300-hour speed perturbed Switchboard corpus trained LF-MMI TDNN/CNN-TDNN systems suggest the proposed Bayesian adaptation approaches consistently outperform the deterministic adaptation on the NIST Hub5'00 and RT03 evaluation sets. When using only the first five utterances from each speaker as adaptation data, significant word error rate reductions up to 1.4% absolute (7.2% relative) were obtained on the CallHome subset. The efficacy of the proposed Bayesian adaptation techniques is further demonstrated in a comparison against the state-of-the-art performance obtained on the same task using the most recent systems reported in the literature.
We present BOFFIN TTS (Bayesian Optimization For FIne-tuning Neural Text To Speech), a novel approach for few-shot speaker adaptation. Here, the task is to fine-tune a pre-trained TTS model to mimic a new speaker using a small corpus of target utterances. We demonstrate that there does not exist a one-size-fits-all adaptation strategy, with convincing synthesis requiring a corpus-specific configuration of the hyper-parameters that control fine-tuning. By using Bayesian optimization to efficiently optimize these hyper-parameter values for a target speaker, we are able to perform adaptation with…
Université Laval（拉瓦尔大学）；Univ. of St-Etienne（圣艾蒂安大学）
This paper provides a theoretical analysis of domain adaptation based on the PAC-Bayesian theory. We propose an improvement of the previous domain adaptation bound obtained by Germain et al. in two ways. We first give another generalization bound tighter and easier to interpret. Moreover, we provide a new analysis of the constant term appearing in the bound that can be of high interest for developing new algorithmic solutions.
Population attributes are essential in health for understanding who the data represents and precision medicine efforts. Even within disease infection labels, patients can exhibit significant variability; "fever" may mean something different when reported in a doctor's office versus from an online app, precluding directly learning across different datasets for the same prediction task. This problem falls into the domain adaptation paradigm. However, research in this area has to-date not considered who generates the data; symptoms reported by a woman versus a man, for example, could also have di…
In this paper, we provide two main contributions in PAC-Bayesian theory for domain adaptation where the objective is to learn, from a source distribution, a well-performing majority vote on a different target distribution. On the one hand, we propose an improvement of the previous approach proposed by Germain et al. (2013), that relies on a novel distribution pseudodistance based on a disagreement averaging, allowing us to derive a new tighter PAC-Bayesian domain adaptation bound for the stochastic Gibbs classifier. We specialize it to linear classifiers, and design a learning algorithm which …
In the need for low assumption inferential methods in infinite-dimensional settings, Bayesian adaptive estimation via a prior distribution that does not depend on the regularity of the function to be estimated nor on the sample size is valuable. We elucidate relationships among the main approaches followed to design priors for minimax-optimal rate-adaptive estimation meanwhile shedding light on the underlying ideas.
INRIA, SIERRA Project-Team（法国国家信息与自动化研究所，SIERRA项目组）；D.I., Ecole Normale Superieure（巴黎高等师范学校计算机科学系）；Univ Lyon, UJM-Saint-Etienne, CNRS, IOGS, Laboratoire Hubert Curien UMR 5516（里昂大学，圣艾蒂安让·莫内大学，法国国家科学研究中心，IOGS，于贝尔·居里安实验室）；Université Laval（拉瓦尔大学）
We study the issue of PAC-Bayesian domain adaptation: We want to learn, from a source domain, a majority vote model dedicated to a target one. Our theoretical contribution brings a new perspective by deriving an upper-bound on the target risk where the distributions' divergence---expressed as a ratio---controls the trade-off between a source error measure and the target voters' disagreement. Our bound suggests that one has to focus on regions where the source data is informative.From this result, we derive a PAC-Bayesian generalization bound, and specialize it to linear classifiers. Then, we i…
This paper studies a Bayesian approach to non-asymptotic minimax adaptation in nonparametric estimation. Estimating an input function on the basis of output functions in a Gaussian white-noise model is discussed. The input function is assumed to be in a Sobolev ellipsoid with an unknown smoothness and an unknown radius. Our purpose in this paper is to present a Bayesian approach attaining minimaxity up to a universal constant without any knowledge regarding the smoothness and the radius. Our Bayesian approach provides not only a rate-exact minimax adaptive estimator in large sample asymptotics…
Quantum state tomography, an important task in quantum information processing, aims at reconstructing a state from prepared measurement data. Bayesian methods are recognized to be one of the good and reliable choice in estimating quantum states~\cite{blume2010optimal}. Several numerical works showed that Bayesian estimations are comparable to, and even better than other methods in the problem of $1$-qubit state recovery. However, the problem of choosing prior distribution in the general case of $n$ qubits is not straightforward. More importantly, the statistical performance of Bayesian type es…
Qiushi Academy for Advanced Studies, Zhejiang University（浙江大学求是高等研究院）；College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；State University of New York at Buffalo（纽约州立大学布法罗分校）；Zhejiang University School of Medicine（浙江大学医学院）
Domain adaptation is an important technique to alleviate performance degradation caused by domain shift, e.g., when training and test data come from different domains. Most existing deep adaptation methods focus on reducing domain shift by matching marginal feature distributions through deep transformations on the input features, due to the unavailability of target domain labels. We show that domain shift may still exist via label distribution shift at the classifier, thus deteriorating model performances. To alleviate this issue, we propose an approximate joint distribution matching scheme by…
A novel block prior is proposed for adaptive Bayesian estimation. The prior does not depend on the smoothness of the function or the sample size. It puts sufficient prior mass near the true signal and automatically concentrates on its effective dimension. A rate-optimal posterior contraction is obtained in a general framework, which includes density estimation, white noise model, Gaussian sequence model, Gaussian regression and spectral density estimation.
Indian Institute of Technology, Kanpur（印度理工学院坎普尔分校）
Continual Learning is a learning paradigm where learning systems are trained with sequential or streaming tasks. Two notable directions among the recent advances in continual learning with neural networks are ($i$) variational Bayes based regularization by learning priors from previous tasks, and, ($ii$) learning the structure of deep networks to adapt to new tasks. So far, these two approaches have been orthogonal. We present a novel Bayesian approach to continual learning based on learning the structure of deep neural networks, addressing the shortcomings of both these approaches. The propos…
This paper is considered with joint estimation of state and time-varying noise covariance matrices in non-linear stochastic state space models. We present a variational Bayes and Gaussian filtering based algorithm for efficient computation of the approximate filtering posterior distributions. The Gaussian filtering based formulation of the non-linear state space model computation allows usage of efficient Gaussian integration methods such as unscented transform, cubature integration and Gauss-Hermite integration along with the classical Taylor series approximations. The performance of the algo…
Many real-life applications involve estimation of curves that exhibit complicated shapes including jumps or varying-frequency oscillations. Practical methods have been devised that can adapt to a locally varying complexity of an unknown function (e.g. variable-knot splines, sparse wavelet reconstructions, kernel methods or trees/forests). However, the overwhelming majority of existing asymptotic minimaxity theory is predicated on homogeneous smoothness assumptions. Focusing on locally Holderian functions, we provide new locally adaptive posterior concentration rate results under the supremum l…
This article reviews how organisms learn and recognize the world through the dynamics of neural networks from the perspective of Bayesian inference, and introduces a view on how such dynamics is described by the laws for the entropy of neural activity, a paradigm that we call thermodynamics of the Bayesian brain. The Bayesian brain hypothesis sees the stimulus-evoked activity of neurons as an act of constructing the Bayesian posterior distribution based on the generative model of the external world that an organism possesses. A closer look at the stimulus-evoked activity at early sensory corti…
Université Laval（拉瓦尔大学）；Laboratoire Hubert Curien UMR CNRS 5516（于贝尔·居里安实验室 CNRS UMR 5516）；Univ. Jean Monnet（让·莫内大学）；Aix-Marseille Univ.（艾克斯-马赛大学）；CNRS（法国国家科学研究中心）
In machine learning, Domain Adaptation (DA) arises when the distribution gen- erating the test (target) data differs from the one generating the learning (source) data. It is well known that DA is an hard task even under strong assumptions, among which the covariate-shift where the source and target distributions diverge only in their marginals, i.e. they have the same labeling function. Another popular approach is to consider an hypothesis class that moves closer the two distributions while implying a low-error for both tasks. This is a VC-dim approach that restricts the complexity of an hypo…
In recent years, there has been increasing amount of interest around meta reinforcement learning methods for traffic signal control, which have achieved better performance compared with traditional control methods. However, previous methods lack robustness in adaptation and stability in training process in complex situations, which largely limits its application in real-world traffic signal control. In this paper, we propose a novel value-based Bayesian meta-reinforcement learning framework BM-DQN to robustly speed up the learning process in new scenarios by utilizing well-trained prior knowle…
A central part of population genomics consists of finding genomic regions implicated in local adaptation. Population genomic analyses are based on genotyping numerous molecular markers and looking for outlier loci in terms of patterns of genetic differentiation. One of the most common approach for selection scan is based on statistics that measure population differentiation such as $F_{ST}$. However they are important caveats with approaches related to $F_{ST}$ because they require grouping individuals into populations and they additionally assume a particular model of population structure. He…
Google（谷歌）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；XaiPient
We consider representation learning (hypothesis class $\mathcal{H} = \mathcal{F}\circ\mathcal{G}$) where training and test distributions can be different. Recent studies provide hints and failure examples for domain invariant representation learning, a common approach for this problem, but the explanations provided are somewhat different and do not provide a unified picture. In this paper, we provide new decompositions of risk which give finer-grained explanations and clarify potential generalization issues. For Single-Source Domain Adaptation, we give an exact decomposition (an equality) of t…
We introduce a methodology for robust Bayesian estimation with robust divergence (e.g., density power divergence or γ-divergence), indexed by a single tuning parameter. It is well known that the posterior density induced by robust divergence gives highly robust estimators against outliers if the tuning parameter is appropriately and carefully chosen. In a Bayesian framework, one way to find the optimal tuning parameter would be using evidence (marginal likelihood). However, we numerically illustrate that evidence induced by the density power divergence does not work to select the optimal tunin…
Dropout has recently emerged as a powerful and simple method for training neural networks preventing co-adaptation by stochastically omitting neurons. Dropout is currently not grounded in explicit modelling assumptions which so far has precluded its adoption in Bayesian modelling. Using Bayesian entropic reasoning we show that dropout can be interpreted as optimal inference under constraints. We demonstrate this on an analytically tractable regression model providing a Bayesian interpretation of its mechanism for regularizing and preventing co-adaptation as well as its connection to other Baye…
While machine learning is rapidly being developed and deployed in health settings such as influenza prediction, there are critical challenges in using data from one environment in another due to variability in features; even within disease labels there can be differences (e.g. "fever" may mean something different reported in a doctor's office versus in an online app). Moreover, models are often built on passive, observational data which contain different distributions of population subgroups (e.g. men or women). Thus, there are two forms of instability between environments in this observationa…
Land cover maps are a vital input variable to many types of environmental research and management. While they can be produced automatically by machine learning techniques, these techniques require substantial training data to achieve high levels of accuracy, which are not always available. One technique researchers use when labelled training data are scarce is domain adaptation (DA) -- where data from an alternate region, known as the source domain, are used to train a classifier and this model is adapted to map the study region, or target domain. The scenario we address in this paper is known…
We propose a flexible design for the identification of optimal dose combinations in dual-agent dose-finding clinical trials. The design is called AAA, standing for three adaptations: adaptive model selection, adaptive dose insertion, and adaptive cohort divi- sion. The adaptations highlight the need and opportunity for innovation for dual-agent dose finding, and are supported by the numerical results presented in the proposed simulation studies. To our knowledge, this is the first design that allows for all three adaptations at the same time. We find that AAA improves the statistical inference…
Norwegian University of Science and Technology（挪威科技大学）；Delft University of Technology（代尔夫特理工大学）
This article investigates the optimization of yaw control inputs of a nine-turbine wind farm. The wind farm is simulated using the high-fidelity simulator SOWFA. The optimization is performed with a modifier adaptation scheme based on Gaussian processes. Modifier adaptation corrects for the mismatch between plant and model and helps to converge to the actual plan optimum. In the case study the modifier adaptation approach is compared with the Bayesian optimization approach. Moreover, the use of two different covariance functions in the Gaussian process regression is discussed. Practical recomm…
In games, as well as many user-facing systems, adapting content to users' preferences and experience is an important challenge. This paper explores a novel method to realize this goal in the context of dynamic difficulty adjustment (DDA). Here the aim is to constantly adapt the content of a game to the skill level of the player, keeping them engaged by avoiding states that are either too difficult or too easy. Current systems for DDA rely on expensive data mining, or on hand-crafted rules designed for particular domains, and usually adapts to keep players in the flow, leaving no room for the d…
While the choice of prior is one of the most critical parts of the Bayesian inference workflow, recent Bayesian deep learning models have often fallen back on vague priors, such as standard Gaussians. In this review, we highlight the importance of prior choices for Bayesian deep learning and present an overview of different priors that have been proposed for (deep) Gaussian processes, variational autoencoders, and Bayesian neural networks. We also outline different methods of learning priors for these models from data. We hope to motivate practitioners in Bayesian deep learning to think more c…
Recently, S. Arlot and R. Genuer have shown that a model of random forests outperforms its single-tree counterpart in the estimation of $α-$Hölder functions, $α\leq2$. This backs up the idea that ensembles of tree estimators are smoother estimators than single trees. On the other hand, most positive optimality results on Bayesian tree-based methods assume that $α\leq1$. Naturally, one wonders whether Bayesian counterparts of forest estimators are optimal on smoother classes, just like it has been observed for frequentist estimators for $α\leq 2$. We dwell on the problem of density estimation a…
Quantile regression is a powerful data analysis tool that accommodates heterogeneous covariate-response relationships. We find that by coupling the asymmetric Laplace working likelihood with appropriate shrinkage priors, we can deliver posterior inference that automatically adapts to possible sparsity in quantile regression analysis. After a suitable adjustment on the posterior variance, the posterior inference provides asymptotically valid inference under heterogeneity. Furthermore, the proposed approach leads to oracle asymptotic efficiency for the active (nonzero) quantile regression coeffi…
We learn multiple hypotheses for related tasks under a latent hierarchical relationship between tasks. We exploit the intuition that for domain adaptation, we wish to share classifier structure, but for multitask learning, we wish to share covariance structure. Our hierarchical model is seen to subsume several previously proposed multitask learning models and performs well on three distinct real-world data sets.
One of the main challenges of deep learning tools is their inability to capture model uncertainty. While Bayesian deep learning can be used to tackle the problem, Bayesian neural networks often require more time and computational power to train than deterministic networks. Our work explores whether fully Bayesian networks are needed to successfully capture model uncertainty. We vary the number and position of Bayesian layers in a network and compare their performance on active learning with the MNIST dataset. We found that we can fully capture the model uncertainty by using only a few Bayesian…
Determining causes of deaths (COD) occurred outside of civil registration and vital statistics systems is challenging. A technique called verbal autopsy (VA) is widely adopted to gather information on deaths in practice. A VA consists of interviewing relatives of a deceased person about symptoms of the deceased in the period leading to the death, often resulting in multivariate binary responses. While statistical methods have been devised for estimating the cause-specific mortality fractions (CSMFs) for a study population, continued expansion of VA to new populations (or "domains") necessitate…
Tsinghua University（清华大学）；University of Toronto（多伦多大学）
In this paper we introduce ZhuSuan, a python probabilistic programming library for Bayesian deep learning, which conjoins the complimentary advantages of Bayesian methods and deep learning. ZhuSuan is built upon Tensorflow. Unlike existing deep learning libraries, which are mainly designed for deterministic neural networks and supervised tasks, ZhuSuan is featured for its deep root into Bayesian inference, thus supporting various kinds of probabilistic models, including both the traditional hierarchical Bayesian models and recent deep generative models. We use running examples to illustrate th…
We show that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models. We further demonstrate that this finding allows us to make meaningful estimates of the model uncertainty using conventional architectures, without modifications to the network or the training procedure. Our approach is thoroughly validated by measuring the quality of uncertainty in a series of empirical experiments on different tasks. It outperforms baselines with strong statistical significance, and displays competitive performance with recent Bayesian approaches.
The problem of state estimation for unobservable distribution systems is considered. A deep learning approach to Bayesian state estimation is proposed for real-time applications. The proposed technique consists of distribution learning of stochastic power injection, a Monte Carlo technique for the training of a deep neural network for state estimation, and a Bayesian bad-data detection and filtering algorithm. Structural characteristics of the deep neural networks are investigated. Simulations illustrate the accuracy of Bayesian state estimation for unobservable systems and demonstrate the ben…
Probabilistic Geometric Alignment via Bayesian Latent Transport for Domain-Adaptive Foundation Models
School of Information, Computer；Communication Technology Sirindhorn International Institute of Technology, Thammasat University Pathumthani, Thailand 0009-0006-4313-7359；epartment of Architecture, Faculty of Architecture Khon Kaen University Khon Kaen, Thailand
Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually over-parameterized space. This paper investigates a new line of Bayesian deep learning by performing Bayesian inference on network structure. Instead of building structure from scratch inefficiently, we draw inspirations from neural architecture search to represent the network structure. We then develop an efficient stochastic variational inference approach which unifie…
Deep ensembles can be considered as the current state-of-the-art for uncertainty quantification in deep learning. While the approach was originally proposed as a non-Bayesian technique, arguments supporting its Bayesian footing have been put forward as well. We show that deep ensembles can be viewed as an approximate Bayesian method by specifying the corresponding assumptions. Our findings lead to an improved approximation which results in an enlarged epistemic part of the uncertainty. Numerical examples suggest that the improved approximation can lead to more reliable uncertainties. Analytica…
Recent advances in deep reinforcement learning have made significant strides in performance on applications such as Go and Atari games. However, developing practical methods to balance exploration and exploitation in complex domains remains largely unsolved. Thompson Sampling and its extension to reinforcement learning provide an elegant approach to exploration that only requires access to posterior samples of the model. At the same time, advances in approximate Bayesian methods have made posterior approximation for flexible neural network models practical. Thus, it is attractive to consider a…
Learning in deep models using Bayesian methods has generated significant attention recently. This is largely because of the feasibility of modern Bayesian methods to yield scalable learning and inference, while maintaining a measure of uncertainty in the model parameters. Stochastic gradient MCMC algorithms (SG-MCMC) are a family of diffusion-based sampling methods for large-scale Bayesian learning. In SG-MCMC, multivariate stochastic gradient thermostats (mSGNHT) augment each parameter of interest, with a momentum and a thermostat variable to maintain stationary distributions as target poster…
Jilin University（吉林大学）；Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education（教育部符号计算与知识工程重点实验室）
Bayesian optimization (BO) is an effective method of finding the global optima of black-box functions. Recently BO has been applied to neural architecture search and shows better performance than pure evolutionary strategies. All these methods adopt Gaussian processes (GPs) as surrogate function, with the handcraft similarity metrics as input. In this work, we propose a Bayesian graph neural network as a new surrogate, which can automatically extract features from deep neural architectures, and use such learned features to fit and characterize black-box objectives and their uncertainty. Based …
Sequential Kalman Tuning of the $t$-preconditioned Crank-Nicolson algorithm: efficient, adaptive and gradient-free inference for Bayesian inverse problems
University of Western Australia（西澳大学）；Murdoch University（莫道克大学）；Monash University（莫纳什大学）
Modern deep learning methods constitute incredibly powerful tools to tackle a myriad of challenging problems. However, since deep learning methods operate as black boxes, the uncertainty associated with their predictions is often challenging to quantify. Bayesian statistics offer a formalism to understand and quantify the uncertainty associated with deep neural network predictions. This tutorial provides an overview of the relevant literature and a complete toolset to design, implement, train, use and evaluate Bayesian Neural Networks, i.e. Stochastic Artificial Neural Networks trained using B…
Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explicitly Bayesian regularizations in a specific category of DNNs, i.e., Convolutional Neural Networks (CNNs). First, we introduce a novel probabilistic representation for the hidden layers of CNNs and demonstrate that CNNs correspond to Bayesian networks with the serial connection. Furthermore, we show that the hidden layers close to the input formulate prior distributions, thus CN…
We propose a deep generative factor analysis model with beta process prior that can approximate complex non-factorial distributions over the latent codes. We outline a stochastic EM algorithm for scalable inference in a specific instantiation of this model and present some preliminary results.
Courant Institute of Mathematical Sciences（柯朗数学科学研究所）；Center for Data Science（数据科学中心）；New York University（纽约大学）
The key distinguishing property of a Bayesian approach is marginalization instead of optimization, not the prior, or Bayes rule. Bayesian inference is especially compelling for deep neural networks. (1) Neural networks are typically underspecified by the data, and can represent many different but high performing models corresponding to different settings of parameters, which is exactly when marginalization will make the biggest difference for both calibration and accuracy. (2) Deep ensembles have been mistaken as competing approaches to Bayesian methods, but can be seen as approximate Bayesian…
Taiyuan University of Technology（太原理工大学）；Beihang University（北京航空航天大学）
We present a new method to approximate posterior probabilities of Bayesian Network using Deep Neural Network. Experiment results on several public Bayesian Network datasets shows that Deep Neural Network is capable of learning joint probability distri- bution of Bayesian Network by learning from a few observation and posterior probability distribution pairs with high accuracy. Compared with traditional approximate method likelihood weighting sampling algorithm, our method is much faster and gains higher accuracy in medium sized Bayesian Network. Another advantage of our method is that our meth…
Université Laval（拉瓦尔大学）；Inria（法国国家信息与自动化研究所）；University College London（伦敦大学学院）
We present a comprehensive study of multilayer neural networks with binary activation, relying on the PAC-Bayesian theory. Our contributions are twofold: (i) we develop an end-to-end framework to train a binary activated deep neural network, (ii) we provide nonvacuous PAC-Bayesian generalization bounds for binary activated deep neural networks. Our results are obtained by minimizing the expected loss of an architecture-dependent aggregation of binary activated deep neural networks. Our analysis inherently overcomes the fact that binary activation function is non-differentiable. The performance…
