The slowness principle is a concept inspired by the visual cortex of the brain. It postulates that the underlying generative factors of a quickly varying sensory signal change on a slower time scale. Unsupervised learning of intermediate representations utilizing abundant unlabeled sensory data can be leveraged to perform data-efficient supervised downstream regression. In this paper, we propose a general formulation of slowness for unsupervised representation learning adding a slowness regularization term to the estimate lower bound of the beta-VAE to encourage temporal similarity in observation and latent space. Within this framework we compare existing slowness regularization terms such as the L1 and L2 loss used in existing end-to-end methods, the SlowVAE and propose a new term based on Brownian motion. We empirically evaluate these slowness regularization terms with respect to their downstream task performance and data efficiency. We find that slow representations lead to equal or better downstream task performance and data efficiency in different experiment domains when compared to representations without slowness regularization. Finally, we discuss how the Frechet Inception Distance (FID), traditionally used to determine the generative capabilities of GANs, can serve as a measure to predict the performance of pre-trained Autoencoder model in a supervised downstream task and accelerate hyperparameter search.
Massachusetts Institute of Technology（麻省理工学院）；Stanford University（斯坦福大学）；UC Berkeley（加州大学伯克利分校）
Autoregressive models are widely used for tasks such as image and audio generation. The sampling process of these models, however, does not allow interruptions and cannot adapt to real-time computational resources. This challenge impedes the deployment of powerful autoregressive models, which involve a slow sampling process that is sequential in nature and typically scales linearly with respect to the data dimension. To address this difficulty, we propose a new family of autoregressive models that enables anytime sampling. Inspired by Principal Component Analysis, we learn a structured represe…
University of Oxford（牛津大学）；Imperial College London（帝国理工学院）；University of Twente（特文特大学）
We rigorously prove that deep Gaussian process priors can outperform Gaussian process priors if the target function has a compositional structure. To this end, we study information-theoretic lower bounds for posterior contraction rates for Gaussian process regression in a continuous regression model. We show that if the true function is a generalized additive function, then the posterior based on any mean-zero Gaussian process can only recover the truth at a rate that is strictly slower than the minimax rate by a factor that is polynomially suboptimal in the sample size $n$.
Excellent variational approximations to Gaussian process posteriors have been developed which avoid the $\mathcal{O}\left(N^3\right)$ scaling with dataset size $N$. They reduce the computational cost to $\mathcal{O}\left(NM^2\right)$, with $M\ll N$ being the number of inducing variables, which summarise the process. While the computational cost seems to be linear in $N$, the true complexity of the algorithm depends on how $M$ must increase to ensure a certain quality of approximation. We address this by characterising the behavior of an upper bound on the KL divergence to the posterior. We sho…
IBM Research UK（英国IBM研究部）；Sci-Tech Daresbury（科技达尔斯伯里（Sci-Tech Daresbury））；Warrington, UK（英国沃灵顿（Warrington, UK）（注：此处为地址，非机构，按要求不应提取））
Much of machine learning relies on the use of large amounts of data to train models to make predictions. When this data comes from multiple sources, for example when evaluation of data against a machine learning model is offered as a service, there can be privacy issues and legal concerns over the sharing of data. Fully homomorphic encryption (FHE) allows data to be computed on whilst encrypted, which can provide a solution to the problem of data privacy. However, FHE is both slow and restrictive, so existing algorithms must be manipulated to make them work efficiently under the FHE paradigm. …
Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we introduce subsampled tensor projected gradient to solve the problem. Our algorithm is impressively simple and efficient. It is built upon projected gradient method with fast tensor power iterations, leveraging randomized sketching for further acceleration. Theoretical analysis shows that our algorithm converges to the correct solution in fixed number of iteration…
Sony Group Corporation（索尼集团公司）；Sony Europe B.V.（索尼欧洲有限公司）
Federated Learning (FL) allows a number of agents to participate in training a global machine learning model without disclosing locally stored data. Compared to traditional distributed learning, the heterogeneity (non-IID) of the agents slows down the convergence in FL. Furthermore, many datasets, being too noisy or too small, are easily overfitted by complex models, such as deep neural networks. Here, we consider the problem of using FL regression on noisy, hierarchical and tabular datasets in which user distributions are significantly different. Inspired by Latent Class Regression (LCR), we …
Microsoft Research（微软研究院）；Carnegie Mellon University（卡内基梅隆大学）
We introduce data structures for solving robust regression through stochastic gradient descent (SGD) by sampling gradients with probability proportional to their norm, i.e., importance sampling. Although SGD is widely used for large scale machine learning, it is well-known for possibly experiencing slow convergence rates due to the high variance from uniform sampling. On the other hand, importance sampling can significantly decrease the variance but is usually difficult to implement because computing the sampling probabilities requires additional passes over the data, in which case standard gr…
Accurate mobile traffic forecast is important for efficient network planning and operations. However, existing traffic forecasting models have high complexity, making the forecasting process slow and costly. In this paper, we analyze some characteristics of mobile traffic such as periodicity, spatial similarity and short term relativity. Based on these characteristics, we propose a \emph{Block Regression} ({BR}) model for mobile traffic forecasting. This model employs seasonal differentiation so as to take into account of the temporally repetitive nature of mobile traffic. One of the key featu…
University of Žilina（日利纳大学）；Durham University（杜伦大学）；ElaadNL
Here, we develop a data-centric approach enabling to analyse which activities, function, and characteristics of the environment surrounding the slow charging infrastructure impact the distribution of the electricity consumed at slow charging infrastructure. To gain a basic insight, we analysed the probabilistic distribution of energy consumption and its relation to indicators characterizing charging events. We collected geospatial datasets and utilizing statistical methods for data pre-processing, we prepared features modelling the spatial context in which the charging infrastructure operates.…
Case Western Reserve University（凯斯西储大学）；Florida International University（佛罗里达国际大学）；Kent State University（肯特州立大学）；National Institute on Aging, National Institute of Health（美国国立卫生研究院国家老龄化研究所）；Fordham University（福特汉姆大学）
This paper presents a sublinear classical algorithm for principal component regression. The algorithm uses quantum-inspired linear algebra, an idea developed by Tang. Using this technique, her algorithm for recommendation systems achieved runtime only polynomially slower than its quantum counterpart. Her work was quickly adapted to solve many other problems in sublinear time complexity. In this work, we developed an algorithm for principal component regression that runs in time polylogarithmic to the number of data points, an exponential speed up over the state-of-the-art algorithm, under the …
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）
As the data size in Machine Learning fields grows exponentially, it is inevitable to accelerate the computation by utilizing the ever-growing large number of available cores provided by high-performance computing hardware. However, existing parallel methods for clustering or regression often suffer from problems of low accuracy, slow convergence, and complex hyperparameter-tuning. Furthermore, the parallel efficiency is usually difficult to improve while striking a balance between preserving model properties and partitioning computing workloads on distributed systems. In this paper, we propose…
Department of Electrical Engineering, University of Southern California（南加州大学电气工程系（University of Southern California 为南加州大学））
We consider the problem of training a least-squares regression model on a large dataset using gradient descent. The computation is carried out on a distributed system consisting of a master node and multiple worker nodes. Such distributed systems are significantly slowed down due to the presence of slow-running machines (stragglers) as well as various communication bottlenecks. We propose "polynomially coded regression" (PCR) that substantially reduces the effect of stragglers and lessens the communication burden in such systems. The key idea of PCR is to encode the partial data stored at each…
We propose robust sparse reduced rank regression for analyzing large and complex high-dimensional data with heavy-tailed random noise. The proposed method is based on a convex relaxation of a rank- and sparsity-constrained non-convex optimization problem, which is then solved using the alternating direction method of multipliers algorithm. We establish non-asymptotic estimation error bounds under both Frobenius and nuclear norms in the high-dimensional setting. This is a major contribution over existing results in reduced rank regression, which mainly focus on rank selection and prediction con…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Microsoft（微软）
We study in this paper how to initialize the parameters of multinomial logistic regression (a fully connected layer followed with softmax and cross entropy loss), which is widely used in deep neural network (DNN) models for classification problems. As logistic regression is widely known not having a closed-form solution, it is usually randomly initialized, leading to several deficiencies especially in transfer learning where all the layers except for the last task-specific layer are initialized using a pre-trained model. The deficiencies include slow convergence speed, possibility of stuck in …
Regularization is used to find a solution that both fits the data and is sufficiently smooth, and thereby is very effective for designing and refining learning algorithms. But the influence of its exponent remains poorly understood. In particular, it is unclear how the exponent of the reproducing kernel Hilbert space~(RKHS) regularization term affects the accuracy and the efficiency of kernel-based learning algorithms. Here we consider regularized least squares regression (RLSR) with an RKHS regularization raised to the power of m, where m is a variable real exponent. We design an efficient al…
Visual representation is crucial for a visual tracking method's performances. Conventionally, visual representations adopted in visual tracking rely on hand-crafted computer vision descriptors. These descriptors were developed generically without considering tracking-specific information. In this paper, we propose to learn complex-valued invariant representations from tracked sequential image patches, via strong temporal slowness constraint and stacked convolutional autoencoders. The deep slow local representations are learned offline on unlabeled data and transferred to the observational mode…
Bayesian Data Sketching for Varying Coefficient Regression Models
Department of Statistics Texas A & M University College Station, TX 77843-3143, USA（统计学系，德克萨斯农工大学）；Department of Statistics and Applied Probability University of California Santa Barbara Santa Barbara, CA 93106-3110, USA（统计学与应用概率系，加州大学圣巴巴拉分校）；UCLA Department of Biostatistics University of California Los Angeles Los Angeles, CA 90095-1772, USA（生物统计学系，加州大学洛杉矶分校）
Learning to Simulate: Generative Metamodeling via Quantile Regression
Department of Industrial and Systems Engineering, University of Minnesota（明尼苏达大学工业与系统工程系）；School of Data Science, Fudan University（复旦大学数据科学学院）；School of Management, Fudan University（复旦大学管理学院）；Department of Decision Analytics and Operations, City University of Hong Kong（香港城市大学决策分析与运营系）；Department of Industrial Engineering and Decision Analytics, The Hong Kong University of Science and Technology（香港科技大学工业工程与决策分析系）
Fast Escape, Slow Convergence: Learning Dynamics of Phase Retrieval under Power-Law Data
RIKEN AIP（日本理化学研究所Advanced Institute for Integrated Sciences and Innovation）；École Normale Supérieure, PSL & CNRS（巴黎综合理工学院及国家科学研究中心）；University of Tokyo, RIKEN AIP（东京大学及日本理化学研究所Advanced Institute for Integrated Sciences and Innovation）
Local differential privacy has become the gold-standard of privacy literature for gathering or releasing sensitive individual data points in a privacy-preserving manner. However, locally differential data can twist the probability density of the data because of the additive noise used to ensure privacy. In fact, the density of privacy-preserving data (no matter how many samples we gather) is always flatter in comparison with the density function of the original data points due to convolution with privacy-preserving noise density function. The effect is especially more pronounced when using slo…
