Non-parametric, additive models are able to capture complex data dependencies in a flexible, yet interpretable way. However, choosing the format of the additive components often requires non-trivial data exploration. Here, as an alternative, we propose PrAda-net, a one-hidden-layer neural network, trained with proximal gradient descent and adaptive lasso. PrAda-net automatically adjusts the size and architecture of the neural network to reflect the complexity and structure of the data. The compact network obtained by PrAda-net can be translated to additive model components, making it suitable for non-parametric statistical modelling with automatic model selection. We demonstrate PrAda-net on simulated data, where wecompare the test error performance, variable importance and variable subset identification properties of PrAda-net to other lasso-based regularization approaches for neural networks. We also apply PrAda-net to the massive U.K. black smoke data set, to demonstrate how PrAda-net can be used to model complex and heterogeneous data with spatial and temporal components. In contrast to classical, statistical non-parametric approaches, PrAda-net requires no preliminary modeling to select the functional forms of the additive components, yet still results in an interpretable model representation.
We propose a non-parametric variant of binary regression, where the hypothesis is regularized to be a Lipschitz function taking a metric space to [0,1] and the loss is logarithmic. This setting presents novel computational and statistical challenges. On the computational front, we derive a novel efficient optimization algorithm based on interior point methods; an attractive feature is that it is parameter-free (i.e., does not require tuning an update step size). On the statistical front, the unbounded loss function presents a problem for classic generalization bounds, based on covering-number …
In this work a method to regularize Cox frailty models is proposed that accommodates time-varying covariates and time-varying coefficients and is based on the full instead of the partial likelihood. A particular advantage in this framework is that the baseline hazard can be explicitly modeled in a smooth, semi-parametric way, e.g. via P-splines. Regularization for variable selection is performed via a lasso penalty and via group lasso for categorical variables while a second penalty regularizes wiggliness of smooth estimates of time-varying coefficients and the baseline hazard. Additionally, a…
This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when the covariates are highly correlated. Motivated by econometric studies, we consider the case where covariate dependence can be reduced through factor model, and propose a consistent strategy named Factor-Adjusted Regularized Model Selection (FarmSelect). By separating the latent factors from idiosyncratic components, we transform the problem from model sele…
We consider the maximum mean discrepancy ($\mathrm{MMD}$) GAN problem and propose a parametric kernelized gradient flow that mimics the min-max game in gradient regularized $\mathrm{MMD}$ GAN. We show that this flow provides a descent direction minimizing the $\mathrm{MMD}$ on a statistical manifold of probability distributions. We then derive an explicit condition which ensures that gradient descent on the parameter space of the generator in gradient regularized $\mathrm{MMD}$ GAN is globally convergent to the target distribution. Under this condition, we give non asymptotic convergence resul…
This paper analyzes a new regularized learning scheme for high dimensional partially linear support vector machine. The proposed approach consists of an empirical risk and the Lasso-type penalty for linear part, as well as the standard functional norm for nonlinear part. Here the linear kernel is used for model interpretation and feature selection, while the nonlinear kernel is adopted to enhance algorithmic flexibility. In this paper, we develop a new technical analysis on the weighted empirical process, and establish the sharp learning rates for the semi-parametric estimator under the regula…
Variational problems that involve Wasserstein distances and more generally optimal transport (OT) theory are playing an increasingly important role in data sciences. Such problems can be used to form an examplar measure out of various probability measures, as in the Wasserstein barycenter problem, or to carry out parametric inference and density fitting, where the loss is measured in terms of an optimal transport cost to the measure of observations. Despite being conceptually simple, such problems are computationally challenging because they involve minimizing over quantities (Wasserstein dist…
The R package spikeSlabGAM implements Bayesian variable selection, model choice, and regularized estimation in (geo-)additive mixed models for Gaussian, binomial, and Poisson responses. Its purpose is to (1) choose an appropriate subset of potential covariates and their interactions, (2) to determine whether linear or more flexible functional forms are required to model the effects of the respective covariates, and (3) to estimate their shapes. Selection and regularization of the model terms is based on a novel spike-and-slab-type prior on coefficient groups associated with parametric and semi…
Generalized canonical correlation analysis (GCCA) aims at finding latent low-dimensional common structure from multiple views (feature vectors in different domains) of the same entities. Unlike principal component analysis (PCA) that handles a single view, (G)CCA is able to integrate information from different feature spaces. Here we focus on MAX-VAR GCCA, a popular formulation which has recently gained renewed interest in multilingual processing and speech modeling. The classic MAX-VAR GCCA problem can be solved optimally via eigen-decomposition of a matrix that compounds the (whitened) corre…
Partial linear models have been widely used as flexible method for modelling linear components in conjunction with non-parametric ones. Despite the presence of the non-parametric part, the linear, parametric part can under certain conditions be estimated with parametric rate. In this paper, we consider a high-dimensional linear part. We show that it can be estimated with oracle rates, using the LASSO penalty for the linear part and a smoothness penalty for the nonparametric part.
Sandia National Laboratories（桑迪亚国家实验室）；Xilinx Inc.（赛灵思公司）；Georgia Institute of Technology（佐治亚理工学院）
Bayesian optimization (BO) is an efficient and flexible global optimization framework that is applicable to a very wide range of engineering applications. To leverage the capability of the classical BO, many extensions, including multi-objective, multi-fidelity, parallelization, latent-variable model, have been proposed to improve the limitation of the classical BO framework. In this work, we propose a novel multi-objective (MO) extension, called srMO-BO-3GP, to solve the MO optimization problems in a sequential setting. Three different Gaussian processes (GPs) are stacked together, where each…
Simula Metropolitan Center for Digital Engineering（Simula城市数字工程中心）；Oslo Metropolitan University（奥斯陆城市大学）；CNRS（法国国家科学研究中心）；Université de Rennes（雷恩大学）；Inria（法国国家信息与自动化研究所）；IRISA（IRISA研究所）
Coupled matrix and tensor factorizations (CMTF) are frequently used to jointly analyze data from multiple sources, also called data fusion. However, different characteristics of datasets stemming from multiple sources pose many challenges in data fusion and require to employ various regularizations, constraints, loss functions and different types of coupling structures between datasets. In this paper, we propose a flexible algorithmic framework for coupled matrix and tensor factorizations which utilizes Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). T…
Clustering single-cell RNA sequence (scRNA-seq) data poses statistical and computational challenges due to their high-dimensionality and data-sparsity, also known as `dropout' events. Recently, Regularized Auto-Encoder (RAE) based deep neural network models have achieved remarkable success in learning robust low-dimensional representations. The basic idea in RAEs is to learn a non-linear mapping from the high-dimensional data space to a low-dimensional latent space and vice-versa, simultaneously imposing a distributional prior on the latent space, which brings in a regularization effect. This …
University of Oslo（奥斯陆大学）；Norwegian Computing Center（挪威计算中心）；Medical University of Vienna（维也纳医科大学）
Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between input variables and a response. Such relationships can be better described through flexible approaches such as neural networks, but this results in less interpretable models and potential overfitting. Alternatively, specific parametric nonlinear functions can be used, but the specification of such functions is in general complicated. In this paper, we introdu…
We present an off-policy actor-critic algorithm for Reinforcement Learning (RL) that combines ideas from gradient-free optimization via stochastic search with learned action-value function. The result is a simple procedure consisting of three steps: i) policy evaluation by estimating a parametric action-value function; ii) policy improvement via the estimation of a local non-parametric policy; and iii) generalization by fitting a parametric policy. Each step can be implemented in different ways, giving rise to several algorithm variants. Our algorithm draws on connections to existing literatur…
Indian Institute of Technology Bombay（印度理工学院孟买分校）；ENS Paris-Saclay（巴黎-萨克雷高等师范学院）
With the advent of data-driven statistical modeling and abundant computing power, researchers are turning increasingly to deep learning for audio synthesis. These methods try to model audio signals directly in the time or frequency domain. In the interest of more flexible control over the generated sound, it could be more useful to work with a parametric representation of the signal which corresponds more directly to the musical attributes such as pitch, dynamics and timbre. We present VaPar Synth - a Variational Parametric Synthesizer which utilizes a conditional variational autoencoder (CVAE…
A flexible Bayesian non-parametric mixture model reveals multiple dependencies of swap errors in visual working memory
Department of Engineering University of Cambridge（工程系剑桥大学）；Department of Psychology University of Cambridge（心理学系剑桥大学）；Department of Cognitive Science Central European University（认知科学系中央欧亚大学）
In recent years, text-aware collaborative filtering methods have been proposed to address essential challenges in recommendations such as data sparsity, cold start problem, and long-tail distribution. However, many of these text-oriented methods rely heavily on the availability of text information for every user and item, which obviously does not hold in real-world scenarios. Furthermore, specially designed network structures for text processing are highly inefficient for on-line serving and are hard to integrate into current systems. In this paper, we propose a flexible neural recommendation …
Khoury College of Computer Sciences, Northeastern University（东北大学库理计算机学院）；Department of Mathematics, Northeastern University（东北大学数学系）
Generative Adversarial Networks (GANs) have been shown to be powerful and flexible priors when solving inverse problems. One challenge of using them is overcoming representation error, the fundamental limitation of the network in representing any particular signal. Recently, multiple proposed inversion algorithms reduce representation error by optimizing over intermediate layer representations. These methods are typically applied to generative models that were trained agnostic of the downstream inversion algorithm. In our work, we introduce a principle that if a generative model is intended fo…
The Australian National University（澳大利亚国立大学）；Data61 CSIRO（联邦科学与工业研究组织数据61所）；University of Technology Sydney（悉尼科技大学）
In this paper, we develop an efficient nonparametric Bayesian estimation of the kernel function of Hawkes processes. The non-parametric Bayesian approach is important because it provides flexible Hawkes kernels and quantifies their uncertainty. Our method is based on the cluster representation of Hawkes processes. Utilizing the finite support assumption of the Hawkes process, we efficiently sample random branching structures and thus, we split the Hawkes process into clusters of Poisson processes. We derive two algorithms -- a block Gibbs sampler and a maximum a posteriori estimator based on e…
University of Bath（巴斯大学）；University of Bristol（布里斯托尔大学）
We present a non-parametric Bayesian latent variable model capable of learning dependency structures across dimensions in a multivariate setting. Our approach is based on flexible Gaussian process priors for the generative mappings and interchangeable Dirichlet process priors to learn the structure. The introduction of the Dirichlet process as a specific structural prior allows our model to circumvent issues associated with previous Gaussian process latent variable models. Inference is performed by deriving an efficient variational bound on the marginal log-likelihood on the model.
Albert Einstein College of Medicine（阿尔伯特·爱因斯坦医学院）；École Normale Supérieure, PSL University（巴黎高等师范学院，巴黎文理研究大学）
Probabilistic finite mixture models are widely used for unsupervised clustering. These models can often be improved by adapting them to the topology of the data. For instance, in order to classify spatially adjacent data points similarly, it is common to introduce a Laplacian constraint on the posterior probability that each data point belongs to a class. Alternatively, the mixing probabilities can be treated as free parameters, while assuming Gauss-Markov or more complex priors to regularize those mixing probabilities. However, these approaches are constrained by the shape of the prior and of…
In this work we develop a new algorithm for regularized empirical risk minimization. Our method extends recent techniques of Shalev-Shwartz [02/2015], which enable a dual-free analysis of SDCA, to arbitrary mini-batching schemes. Moreover, our method is able to better utilize the information in the data defining the ERM problem. For convex loss functions, our complexity results match those of QUARTZ, which is a primal-dual method also allowing for arbitrary mini-batching schemes. The advantage of a dual-free analysis comes from the fact that it guarantees convergence even for non-convex loss f…
Dept. Information Eng., Electronics and Telecomm., Sapienza University of Rome（罗马一大信息工程、电子与电信系）；Dept. Communications Eng., University of Cantabria（坎塔布里亚大学通信工程系）
Graph neural networks (GNNs) are a class of neural networks that allow to efficiently perform inference on data that is associated to a graph structure, such as, e.g., citation networks or knowledge graphs. While several variants of GNNs have been proposed, they only consider simple nonlinear activation functions in their layers, such as rectifiers or squashing functions. In this paper, we investigate the use of graph convolutional networks (GCNs) when combined with more complex activation functions, able to adapt from the training data. More specifically, we extend the recently proposed kerne…
The recurrent neural networks (RNN) with richly distributed internal states and flexible non-linear transition functions, have overtaken the dynamic Bayesian networks such as the hidden Markov models (HMMs) in the task of modeling highly structured sequential data. These data, such as from speech and handwriting, often contain complex relationships between the underlaying variational factors and the observed data. The standard RNN model has very limited randomness or variability in its structure, coming from the output conditional probability model. This paper will present different ways of us…
Many previous proposals for adversarial training of deep neural nets have included di- rectly modifying the gradient, training on a mix of original and adversarial examples, using contractive penalties, and approximately optimizing constrained adversarial ob- jective functions. In this paper, we show these proposals are actually all instances of optimizing a general, regularized objective we call DataGrad. Our proposed DataGrad framework, which can be viewed as a deep extension of the layerwise contractive au- toencoder penalty, cleanly simplifies prior work and easily allows extensions such a…
University of Massachusetts（马萨诸塞大学）；University of Utah（犹他大学）；University of Campinas（坎皮纳斯大学）；University of Maryland（马里兰大学）
Multitask learning algorithms are typically designed assuming some fixed, a priori known latent structure shared by all the tasks. However, it is usually unclear what type of latent task structure is the most appropriate for a given multitask learning problem. Ideally, the "right" latent task structure should be learned in a data-driven manner. We present a flexible, nonparametric Bayesian model that posits a mixture of factor analyzers structure on the tasks. The nonparametric aspect makes the model expressive enough to subsume many existing models of latent task structures (e.g, mean-regular…
