In this paper we introduce Feature Gradients, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e., in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N . This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Crucially, our algorithm is capable of finding higher-order correlations between features and targets for both the N > D and N < D regimes, as opposed to approaches that do not consider such interactions and/or only consider one regime. We provide experimental demonstration of the algorithm in small and large sample-and feature-size settings.
Classic feature selection techniques remove those features that are either irrelevant or redundant, achieving a subset of relevant features that help to provide a better knowledge extraction. This allows the creation of compact models that are easier to interpret. Most of these techniques work over the whole dataset, but they are unable to provide the user with successful information when only instance information is needed. In short, given any example, classic feature selection algorithms do not give any information about which the most relevant information is, regarding this sample. This wor…
Gradient Boosted Decision Trees (GBDTs) are widely used for building ranking and relevance models in search and recommendation. Considerations such as latency and interpretability dictate the use of as few features as possible to train these models. Feature selection in GBDT models typically involves heuristically ranking the features by importance and selecting the top few, or by performing a full backward feature elimination routine. On-the-fly feature selection methods proposed previously scale suboptimally with the number of features, which can be daunting in high dimensional settings. We …
We study the problem of optimizing expensive blackbox functions over combinatorial spaces (e.g., sets, sequences, trees, and graphs). BOCS (Baptista and Poloczek, 2018) is a state-of-the-art Bayesian optimization method for tractable statistical models, which performs semi-definite programming based acquisition function optimization (AFO) to select the next structure for evaluation. Unfortunately, BOCS scales poorly for large number of binary and/or categorical variables. Based on recent advances in submodular relaxation (Ito and Fujimaki, 2016) for solving Binary Quadratic Programs, we study …
Simon Fraser University（西蒙弗雷泽大学）；Hefei University of Technology（合肥工业大学）；University of Vermont（佛蒙特大学）；University of Massachusetts Boston（马萨诸塞大学波士顿分校）
Feature selection is important in many big data applications. Two critical challenges closely associate with big data. Firstly, in many big data applications, the dimensionality is extremely high, in millions, and keeps growing. Secondly, big data applications call for highly scalable feature selection algorithms in an online manner such that each feature can be processed in a sequential scan. We present SAOLA, a Scalable and Accurate OnLine Approach for feature selection in this paper. With a theoretical analysis on bounds of the pairwise correlations between features, SAOLA employs novel pai…
We present a new approach to learning the structure and parameters of a Bayesian network based on regularized estimation in an exponential family representation. Here we show that, given a fixed variable order, the optimal structure and parameters can be learned efficiently, even without restricting the size of the parent sets. We then consider the problem of optimizing the variable order for a given set of features. This is still a computationally hard problem, but we present a convex relaxation that yields an optimal 'soft' ordering in polynomial time. One novel aspect of the approach is tha…
Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for each greedy step we need to refit a model or calculate a function using the previously selected choices and the new candidate. Two algorithms that are faster approximations to the greedy forward selection were introduced recently ([Mirzasoleiman et al. 2013, 2015]). They achieve better performance by exploiting distributed computation and stochastic evaluat…
Feature selection with large-scale high-dimensional data is important yet very challenging in machine learning and data mining. Online feature selection is a promising new paradigm that is more efficient and scalable than batch feature section methods, but the existing online approaches usually fall short in their inferior efficacy as compared with batch approaches. In this paper, we present a novel second-order online feature selection scheme that is simple yet effective, very fast and extremely scalable to deal with large-scale ultra-high dimensional sparse data streams. The basic idea is to…
scMamba: A Scalable Foundation Model for Single-Cell Multi-Omics Integration Beyond Highly Variable Feature Selection
AI for Science Interdisciplinary Research Center（人工智能科学交叉研究中心）；School of Computer Science, Northwestern Polytechnical University（西北工业大学计算机学院）；Key Laboratory of Big Data Storage and Management, Northwestern Polytechnical University, Ministry of Industry and Information Technology（大数据存储与管理重点实验室，西北工业大学，工业和信息化部）
A number of recent work studied the effectiveness of feature selection using Lasso. It is known that under the restricted isometry properties (RIP), Lasso does not generally lead to the exact recovery of the set of nonzero coefficients, due to the looseness of convex relaxation. This paper considers the feature selection property of nonconvex regularization, where the solution is given by a multi-stage convex relaxation scheme. Under appropriate conditions, we show that the local solution obtained by this procedure recovers the set of nonzero coefficients without suffering from the bias of Las…
ETH Zurich（苏黎世联邦理工学院）；Max Planck ETH Center for Learning Systems（马克斯·普朗克-苏黎世联邦理工学习系统中心）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Cambridge（剑桥大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）
Marginal-likelihood based model-selection, even though promising, is rarely used in deep learning due to estimation difficulties. Instead, most approaches rely on validation data, which may not be readily available. In this work, we present a scalable marginal-likelihood estimation method to select both hyperparameters and network architectures, based on the training data alone. Some hyperparameters can be estimated online during training, simplifying the procedure. Our marginal-likelihood estimate is based on Laplace's method and Gauss-Newton approximations to the Hessian, and it outperforms …
Discrete random variables are natural components of probabilistic clustering models. A number of VAE variants with discrete latent variables have been developed. Training such methods requires marginalizing over the discrete latent variables, causing training time complexity to be linear in the number clusters. By applying a continuous relaxation to the discrete variables in these methods we can achieve a reduction in the training time complexity to be constant in the number of clusters used. We demonstrate that in practice for one such method, the Gaussian Mixture VAE, the use of a continuous…
Variable selection in Gaussian processes (GPs) is typically undertaken by thresholding the inverse lengthscales of automatic relevance determination kernels, but in high-dimensional datasets this approach can be unreliable. A more probabilistically principled alternative is to use spike and slab priors and infer a posterior probability of variable inclusion. However, existing implementations in GPs are very costly to run in both high-dimensional and large-$n$ datasets, or are only suitable for unsupervised settings with specific kernels. As such, we develop a fast and scalable variational infe…
EPFL（洛桑联邦理工学院）；MIT（麻省理工学院）；University of Texas at Austin（得克萨斯大学奥斯汀分校）；IIT Kharagpur（印度理工学院卡拉格普尔分校）
Group-based sparsity models are proven instrumental in linear regression problems for recovering signals from much fewer measurements than standard compressive sensing. The main promise of these models is the recovery of "interpretable" signals through the identification of their constituent groups. In this paper, we establish a combinatorial framework for group-model selection problems and highlight the underlying tractability issues. In particular, we show that the group-model selection problem is equivalent to the well-known NP-hard weighted maximum coverage problem (WMC). Leveraging a grap…
Automating statistical modelling is a challenging problem in artificial intelligence. The Automatic Statistician takes a first step in this direction, by employing a kernel search algorithm with Gaussian Processes (GP) to provide interpretable statistical models for regression problems. However this does not scale due to its $O(N^3)$ running time for the model selection. We propose Scalable Kernel Composition (SKC), a scalable kernel search algorithm that extends the Automatic Statistician to bigger data sets. In doing so, we derive a cheap upper bound on the GP marginal likelihood that sandwi…
Maximum a posteriori (MAP) inference over discrete Markov random fields is a fundamental task spanning a wide spectrum of real-world applications, which is known to be NP-hard for general graphs. In this paper, we propose a novel semidefinite relaxation formulation (referred to as SDR) to estimate the MAP assignment. Algorithmically, we develop an accelerated variant of the alternating direction method of multipliers (referred to as SDPAD-LR) that can effectively exploit the special structure of the new relaxation. Encouragingly, the proposed procedure allows solving SDR for large-scale proble…
Real networks exhibit nontrivial topological features such as heavy-tailed degree distribution, high clustering, and small-worldness. Researchers have developed several generative models for synthesizing artificial networks that are structurally similar to real networks. An important research problem is to identify the generative model that best fits to a target network. In this paper, we investigate this problem and our goal is to select the model that is able to generate graphs similar to a given network instance. By the means of generating synthetic networks with seven outstanding generativ…
The transport literature is dense regarding short-term traffic predictions, up to the scale of 1 hour, yet less dense for long-term traffic predictions. The transport literature is also sparse when it comes to city-scale traffic predictions, mainly because of low data availability. In this work, we report an effort to investigate whether deep learning models can be useful for the long-term large-scale traffic prediction task, while focusing on the scalability of the models. We investigate a city-scale traffic dataset with 14 weeks of speed observations collected every 15 minutes over 1098 segm…
Regularization vs. Relaxation: A conic optimization perspective of statistical variable selection
Department of Mathematics, Washington State University（数学系，华盛顿州立大学）；Department of Statistics, University of Connecticut（统计系，康涅狄格大学）；Department of Industrial and Systems Engineering, University of Wisconsin-Madison（工业与系统工程系，威斯康星大学麦迪逊分校）
Classification in the dissimilarity space has become a very active research area since it provides a possibility to learn from data given in the form of pairwise non-metric dissimilarities, which otherwise would be difficult to cope with. The selection of prototypes is a key step for the further creation of the space. However, despite previous efforts to find good prototypes, how to select the best representation set remains an open issue. In this paper we proposed scalable methods to select the set of prototypes out of very large datasets. The methods are based on genetic algorithms, dissimil…
As an important problem in modern data analytics, classification has witnessed varieties of applications from different domains. Different from conventional classification approaches, fair classification concerns the issues of unintentional biases against the sensitive features (e.g., gender, race). Due to high nonconvexity of fairness measures, existing methods are often unable to model exact fairness, which can cause inferior fair classification outcomes. This paper fills the gap by developing a novel unified framework to jointly optimize accuracy and fairness. The proposed framework is vers…
National University of Singapore（新加坡国立大学）；Shenzhen University（深圳大学）
This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian process regression (SGPR) models. In contrast to existing GP kernel selection algorithms that aim to select only one kernel with the highest model evidence, our proposed VBKS algorithm considers the kernel as a random variable and learns its belief from data such that the uncertainty of the kernel can be interpreted and exploited to avoid overconfident GP predictions. To achieve this, we represent the probabilistic kernel as an additional variational variable in a variational inference (VI) framewo…
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to high dimensionality, explicit comparison with standard Markov chain Monte Carlo methods and illustrations of the potential improvements in efficiency. Simple and concrete intuition is provided for when the novel scheme is expected to outperform standard schemes. When applied to Bayesian variable-selection problems, the novel algorithm is orders of magnitude mo…
Shanghai University of Finance and Economics（上海财经大学）；City University of Hong Kong（香港城市大学）；Nanjing Audit University（南京审计大学）
Variable selection is central to high-dimensional data analysis, and various algorithms have been developed. Ideally, a variable selection algorithm shall be flexible, scalable, and with theoretical guarantee, yet most existing algorithms cannot attain these properties at the same time. In this article, a three-step variable selection algorithm is developed, involving kernel-based estimation of the regression function and its gradient functions as well as a hard thresholding. Its key advantage is that it assumes no explicit model assumption, admits general predictor effects, allows for scalabl…
Gaussian process (GP) regression is a flexible, nonparametric approach to regression that naturally quantifies uncertainty. In many applications, the number of responses and covariates are both large, and a goal is to select covariates that are related to the response. For this setting, we propose a novel, scalable algorithm, coined VGPR, which optimizes a penalized GP log-likelihood based on the Vecchia GP approximation, an ordered conditional approximation from spatial statistics that implies a sparse Cholesky factor of the precision matrix. We traverse the regularization path from strong to…
A Scalable Gradient-Based Optimization Framework for Sparse Minimum-Variance Portfolio Selection
School of Mathematics and Statistics（数学与统计学学院）；University of New South Wales（新南威尔士大学）；School of Mathematical and Physical Sciences（数学与物理科学学院）；University of Technology Sydney（技术大学悉尼分校）；Bayes Business School（贝叶斯商学院）；City St George’s, University of London（伦敦大学城圣乔治学院）；Faculty of Science and Engineering（科学与工程学院）；Macquarie University（麦考瑞大学）
Kernel methods on discrete domains have shown great promise for many challenging data types, for instance, biological sequence data and molecular structure data. Scalable kernel methods like Support Vector Machines may offer good predictive performances but do not intrinsically provide uncertainty estimates. In contrast, probabilistic kernel methods like Gaussian Processes offer uncertainty estimates in addition to good predictive performance but fall short in terms of scalability. While the scalability of Gaussian processes can be improved using sparse inducing point approximations, the selec…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of statistical theory and of scalable algorithms. In this paper, we address the limitations. First, we introduce a convex relaxation of the TT decomposition problem and derive its error bound for the tensor completion task. Next, we develop an alternating optimization method with a randomization technique, in which the time complexity is as efficient as the space compl…
