Inspired by recent developments in learning smoothed densities with empirical Bayes, we study variational autoencoders with a decoder that is tailored for the random variable $Y=X+N(0,σ^2 I_d)$. A notion of smoothed variational inference emerges where the smoothing is implicitly enforced by the noise model of the decoder; "implicit", since during training the encoder only sees clean samples. This is the concept of imaginary noise model, where the noise model dictates the functional form of the variational lower bound $\mathcal{L}(σ)$, but the noisy data are never seen during learning. The model is named $σ$-VAE. We prove that all $σ$-VAEs are equivalent to each other via a simple $β$-VAE expansion: $\mathcal{L}(σ_2) \equiv \mathcal{L}(σ_1,β)$, where $β=σ_2^2/σ_1^2$. We prove a similar result for the Laplace distribution in exponential families. Empirically, we report an intriguing power law $\mathcal{D}_{\rm KL} \sim σ^{-ν}$ for the learned models and we study the inference in the $σ$-VAE for unseen noisy data. The experiments were performed on MNIST, where we show that quite remarkably the model can make reasonable inferences on extremely noisy samples even though it has not seen any during training. The vanilla VAE completely breaks down in this regime. We finish with a hypothesis (the XYZ hypothesis) on the findings here.
A new approach of solving the ill-conditioned inverse problem for analytical continuation is proposed. The root of the problem lies in the fact that even tiny noise of imaginary-time input data has a serious impact on the inferred real-frequency spectra. By means of a modern regularization technique, we eliminate redundant degrees of freedom that essentially carry the noise, leaving only relevant information unaffected by the noise. The resultant spectrum is represented with minimal bases and thus a stable analytical continuation is achieved. This framework further provides a tool for analyzin…
The Chinese University of Hong Kong（香港中文大学）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Huawei Montréal Research Center（华为蒙特利尔研究中心）
The inference of the causal relationship between a pair of observed variables is a fundamental problem in science, and most existing approaches are based on one single causal model. In practice, however, observations are often collected from multiple sources with heterogeneous causal models due to certain uncontrollable factors, which renders causal analysis results obtained by a single model skeptical. In this paper, we generalize the Additive Noise Model (ANM) to a mixture model, which consists of a finite number of ANMs, and provide the condition of its causal identifiability. To conduct mo…
University of Oxford（牛津大学）；University College London（伦敦大学学院）
We show that the gradient estimates used in training Deep Gaussian Processes (DGPs) with importance-weighted variational inference are susceptible to signal-to-noise ratio (SNR) issues. Specifically, we show both theoretically and via an extensive empirical evaluation that the SNR of the gradient estimates for the latent variable's variational parameters decreases as the number of importance samples increases. As a result, these gradient estimates degrade to pure noise if the number of importance samples is too large. To address this pathology, we show how doubly reparameterized gradient estim…
Institute of Mathematics, Technische Universität Berlin（柏林技术大学数学研究所）；Institute of Mathematics, Freie Universität Berlin（柏林自由大学数学研究所）；Bundesanstalt für Materialforschung und Prüfung（材料研究和测试联邦机构）
NAVER AI Lab（NAVER人工智能实验室）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；NAVER Cloud（NAVER云）
The goal of this work is zero-shot text-to-speech synthesis, with speaking styles and voices learnt from facial characteristics. Inspired by the natural fact that people can imagine the voice of someone when they look at his or her face, we introduce a face-styled diffusion text-to-speech (TTS) model within a unified framework learnt from visible attributes, called Face-TTS. This is the first time that face images are used as a condition to train a TTS model. We jointly train cross-model biometrics and TTS models to preserve speaker identity between face images and generated speech segments. W…
Variational Inference for SDEs Driven by Fractional Noise
Ghent University（根特大学）；Flanders Make（法兰德斯制造研究院）；Technical University of Berlin（柏林工业大学）；University of Birmingham（伯明翰大学）；University of Potsdam（波茨坦大学）；Imperial College London（帝国理工学院）
Bayesian analysis for Markov jump processes is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding thus its applicability is limited to a small class of problems. In this paper we describe the application of Riemann manifold MCMC methods using an approximation to the likelihood of the Markov jump process which is valid when the system modelled is near its thermodynamic limit. The proposed approach is both statistically and computationally efficient while the convergence rate and mixing of the chains allows for fast MCMC inf…
Inferring a graphical model or network from observational data from a large number of variables is a well studied problem in machine learning and computational statistics. In this paper we consider a version of this problem that is relevant to the analysis of multiple phenotypes collected in genetic studies. In such datasets we expect correlations between phenotypes and between individuals. We model observations as a sum of two matrix normal variates such that the joint covariance function is a sum of Kronecker products. This model, which generalizes the Graphical Lasso, assumes observations a…
Toyota Technological Institute-Chicago（芝加哥丰田理工学院）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
We analyze a family of methods for statistical causal inference from sample under the so-called Additive Noise Model. While most work on the subject has concentrated on establishing the soundness of the Additive Noise Model, the statistical consistency of the resulting inference methods has received little attention. We derive general conditions under which the given family of inference methods consistently infers the causal direction in a nonparametric setting.
We explore the robustness of recurrent neural networks when the computations within the network are noisy. One of the motivations for looking into this problem is to reduce the high power cost of conventional computing of neural network operations through the use of analog neuromorphic circuits. Traditional GPU/CPU-centered deep learning architectures exhibit bottlenecks in power-restricted applications, such as speech recognition in embedded systems. The use of specialized neuromorphic circuits, where analog signals passed through memory-cell arrays are sensed to accomplish matrix-vector mult…
Georgia Institute of Technology（佐治亚理工学院）；Facebook（脸书）
User-facing software services are becoming increasingly reliant on remote servers to host Deep Neural Network (DNN) models, which perform inference tasks for the clients. Such services require the client to send input data to the service provider, who processes it using a DNN and returns the output predictions to the client. Due to the rich nature of the inputs such as images and speech, the input often contains more information than what is necessary to perform the primary inference task. Consequently, in addition to the primary inference task, a malicious service provider could infer seconda…
Inria（法国国家信息与自动化研究所）；Université Paris-Saclay（巴黎萨克雷大学）；Ecole Normale Supérieure（巴黎高等师范学院）；University of Helsinki（赫尔辛基大学）；HIIT（赫尔辛基信息技术研究所）
We consider a multi-view learning problem known as group independent component analysis (group ICA), where the goal is to recover shared independent sources from many views. The statistical modeling of this problem requires to take noise into account. When the model includes additive noise on the observations, the likelihood is intractable. By contrast, we propose Adaptive multiView ICA (AVICA), a noisy ICA model where each view is a linear mixture of shared independent sources with additive noise on the sources. In this setting, the likelihood has a tractable expression, which enables either …
We propose a new algorithm for training neural networks with binary activations and multi-level weights, which enables efficient processing-in-memory circuits with embedded nonvolatile memories (eNVM). Binary activations obviate costly DACs and ADCs. Multi-level weights leverage multi-level eNVM cells. Compared to existing algorithms, our method not only works for feed-forward networks (e.g., fully-connected and convolutional), but also achieves higher accuracy and noise resilience for recurrent networks. In particular, we present an RNN-based trigger-word detection PIM accelerator, with detai…
The discovery of non-linear causal relationship under additive non-Gaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called least-squares independence regression (LSIR). LSIR learns the additive noise model through the minimization of an estimator of the squared-loss mutual information between inputs and residuals. A notable advantage of LSIR over existing approaches is that tuning parameters such as the kernel width and the regularization parameter can be naturally optimized by cr…
University of Helsinki（赫尔辛基大学）；Aalto University（阿尔托大学）；University of Manchester（曼彻斯特大学）
While generation of synthetic data under differential privacy (DP) has received a lot of attention in the data privacy community, analysis of synthetic data has received much less. Existing work has shown that simply analysing DP synthetic data as if it were real does not produce valid inferences of population-level quantities. For example, confidence intervals become too narrow, which we demonstrate with a simple experiment. We tackle this problem by combining synthetic data analysis techniques from the field of multiple imputation (MI), and synthetic data generation using noise-aware (NA) Ba…
We propose the AdaPtive Noise Augmentation (PANDA) procedure to regularize the estimation and inference of generalized linear models (GLMs). PANDA iteratively optimizes the objective function given noise augmented data until convergence to obtain the regularized model estimates. The augmented noises are designed to achieve various regularization effects, including $l_0$, bridge (lasso and ridge included), elastic net, adaptive lasso, and SCAD, as well as group lasso and fused ridge. We examine the tail bound of the noise-augmented loss function and establish the almost sure convergence of the …
University of California San Diego（加利福尼亚大学圣地亚哥分校）；Arm, Inc.（安谋公司）；Amazon.com, Inc.（亚马逊公司）
A wide variety of deep neural applications increasingly rely on the cloud to perform their compute-heavy inference. This common practice requires sending private and privileged data over the network to remote servers, exposing it to the service provider and potentially compromising its privacy. Even if the provider is trusted, the data can still be vulnerable over communication channels or via side-channel attacks in the cloud. To that end, this paper aims to reduce the information content of the communicated data with as little as possible compromise on the inference accuracy by making the se…
We study two aspects of noisy computations during inference. The first aspect is how to mitigate their side effects for naturally trained deep learning systems. One of the motivations for looking into this problem is to reduce the high power cost of conventional computing of neural networks through the use of analog neuromorphic circuits. Traditional GPU/CPU-centered deep learning architectures exhibit bottlenecks in power-restricted applications (e.g., embedded systems). The use of specialized neuromorphic circuits, where analog signals passed through memory-cell arrays are sensed to accompli…
This paper presents a novel approach for approximate integration over the uncertainty of noise and signal variances in Gaussian process (GP) regression. Our efficient and straightforward approach can also be applied to integration over input dependent noise variance (heteroscedasticity) and input dependent signal variance (nonstationarity) by setting independent GP priors for the noise and signal variances. We use expectation propagation (EP) for inference and compare results to Markov chain Monte Carlo in two simulated data sets and three empirical examples. The results show that EP produces …
Inferring the causal structure of a set of random variables from a finite sample of the joint distribution is an important problem in science. Recently, methods using additive noise models have been suggested to approach the case of continuous variables. In many situations, however, the variables of interest are discrete or even have only finitely many states. In this work we extend the notion of additive noise models to these cases. We prove that whenever the joint distribution $\prob^{(X,Y)}$ admits such a model in one direction, e.g. $Y=f(X)+N, N \independent X$, it does not admit the rever…
State estimations and noise identifications with intermittent corrupted observations via Bayesian variational inference
School of Mathematical Sciences, Beihang University（北京航空航天大学数学科学学院）；Key Laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University（北京航空航天大学数学、信息与行为语义重点实验室（LMIB））
This paper aims to address two fundamental challenges arising in eigenvector estimation and inference for a low-rank matrix from noisy observations: (1) how to estimate an unknown eigenvector when the eigen-gap (i.e. the spacing between the associated eigenvalue and the rest of the spectrum) is particularly small; (2) how to perform estimation and inference on linear functionals of an eigenvector -- a sort of "fine-grained" statistical reasoning that goes far beyond the usual $\ell_2$ analysis. We investigate how to address these challenges in a setting where the unknown $n\times n$ matrix is …
