A common challenge faced in practical supervised learning, such as medical image processing and robotic interactions, is that there are plenty of tasks but each task cannot afford to collect enough labeled examples to be learned in isolation. However, by exploiting the similarities across those tasks, one can hope to overcome such data scarcity. Under a canonical scenario where each task is drawn from a mixture of k linear regressions, we study a fundamental question: can abundant small-data tasks compensate for the lack of big-data tasks? Existing second moment based approaches show that such a trade-off is efficiently achievable, with the help of medium-sized tasks with $Ω(k^{1/2})$ examples each. However, this algorithm is brittle in two important scenarios. The predictions can be arbitrarily bad (i) even with only a few outliers in the dataset; or (ii) even if the medium-sized tasks are slightly smaller with $o(k^{1/2})$ examples each. We introduce a spectral approach that is simultaneously robust under both scenarios. To this end, we first design a novel outlier-robust principal component analysis algorithm that achieves an optimal accuracy. This is followed by a sum-of-squares algorithm to exploit the information from higher order moments. Together, this approach is robust against outliers and achieves a graceful statistical trade-off; the lack of $Ω(k^{1/2})$-size tasks can be compensated for with smaller tasks, which can now be as small as $O(\log k)$.
Londrina State University（隆德里纳州立大学）；University of São Paulo（圣保罗大学）；Federal Technology University（联邦理工大学）
Several multi-target regression methods were devel-oped in the last years aiming at improving predictive performanceby exploring inter-target correlation within the problem. However, none of these methods outperforms the others for all problems. This motivates the development of automatic approachesto recommend the most suitable multi-target regression method. In this paper, we propose a meta-learning system to recommend the best predictive method for a given multi-target regression problem. We performed experiments with a meta-dataset generated by a total of 648 synthetic datasets. These data…
Aalto University（阿尔托大学）；University of Turku（图尔库大学）
This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable by tensors. Hence the function learning problem is transformed into a tensor reconstruction problem, an inverse problem of the tensor decomposition. Our method incrementally builds up the unknown tensor from rank-one terms, which lets us control the complexity of the learned model and reduce the chance of overfitting. For learning the models, we present an …
We begin the study of list-decodable linear regression using batches. In this setting only an $α\in (0,1]$ fraction of the batches are genuine. Each genuine batch contains $\ge n$ i.i.d. samples from a common unknown distribution and the remaining batches may contain arbitrary or even adversarial samples. We derive a polynomial time algorithm that for any $n\ge \tilde Ω(1/α)$ returns a list of size $\mathcal O(1/α^2)$ such that one of the items in the list is close to the true regression parameter. The algorithm requires only $\tilde{\mathcal{O}}(d/α^2)$ genuine batches and works under fairly …
KTH Royal Institute of Technology（瑞典皇家理工学院）；Linköpings University（林雪平大学）
This paper investigates the use of nonparametric kernel-regression to obtain a tasksimilarity aware meta-learning algorithm. Our hypothesis is that the use of tasksimilarity helps meta-learning when the available tasks are limited and may contain outlier/ dissimilar tasks. While existing meta-learning approaches implicitly assume the tasks as being similar, it is generally unclear how this task-similarity could be quantified and used in the learning. As a result, most popular metalearning approaches do not actively use the similarity/dissimilarity between the tasks, but rely on availability of…
We propose MetaNOR, a meta-learnt approach for transfer-learning operators based on the nonlocal operator regression. The overall goal is to efficiently provide surrogate models for new and unknown material-learning tasks with different microstructures. The algorithm consists of two phases: (1) learning a common nonlocal kernel representation from existing tasks; (2) transferring the learned knowledge and rapidly learning surrogate operators for unseen tasks with a different material, where only a few test samples are required. We apply MetaNOR to model the wave propagation within 1D metamater…
This paper addresses the meta-learning problem in sparse linear regression with infinite tasks. We assume that the learner can access several similar tasks. The goal of the learner is to transfer knowledge from the prior tasks to a similar but novel task. For p parameters, size of the support set k , and l samples per task, we show that T \in O (( k log(p) ) /l ) tasks are sufficient in order to recover the common support of all tasks. With the recovered support, we can greatly reduce the sample complexity for estimating the parameter of the novel task, i.e., l \in O (1) with respect to T and …
The strategy of divide-and-combine (DC) has been widely used in the area of big data. Bias-correction is crucial in the DC procedure for validly aggregating the locally biased estimators, especial for the case when the number of batches of data is large. This paper establishes a race-DC through a residual-adjustment composition estimate (race). The race-DC applies to various types of biased estimators, which include but are not limited to Lasso estimator, Ridge estimator and principal component estimator in linear regression, and least squares estimator in nonlinear regression. The resulting g…
University of Washington（华盛顿大学）；Princeton University（普林斯顿大学）；Institute for Advanced Study（高等研究院）
In modern supervised learning, there are a large number of tasks, but many of them are associated with only a small amount of labeled data. These include data from medical image processing and robotic interaction. Even though each individual task cannot be meaningfully trained in isolation, one seeks to meta-learn across the tasks from past experiences by exploiting some similarities. We study a fundamental question of interest: When can abundant tasks with small data compensate for lack of tasks with big data? We focus on a canonical scenario where each task is drawn from a mixture of $k$ lin…
One of the most fundamental aspects of any machine learning algorithm is the training data used by the algorithm. We introduce the novel concept of $ε$-approximation of datasets, obtaining datasets which are much smaller than or are significant corruptions of the original training data while maintaining similar model performance. We introduce a meta-learning algorithm called Kernel Inducing Points (KIP) for obtaining such remarkable datasets, inspired by the recent developments in the correspondence between infinitely-wide neural networks and kernel ridge-regression (KRR). For KRR tasks, we de…
University of Hildesheim（希尔德斯海姆大学）；University of Freiburg（弗莱堡大学）
Meta-learning, or learning to learn, is a machine learning approach that utilizes prior learning experiences to expedite the learning process on unseen tasks. As a data-driven approach, meta-learning requires meta-features that represent the primary learning tasks or datasets, and are estimated traditonally as engineered dataset statistics that require expert domain knowledge tailored for every meta-task. In this paper, first, we propose a meta-feature extractor called Dataset2Vec that combines the versatility of engineered dataset meta-features with the expressivity of meta-features learned b…
École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
We propose regression networks for the problem of few-shot classification, where a classifier must generalize to new classes not seen in the training set, given only a small number of examples of each class. In high dimensional embedding spaces the direction of data generally contains richer information than magnitude. Next to this, state-of-the-art few-shot metric methods that compare distances with aggregated class representations, have shown superior performance. Combining these two insights, we propose to meta-learn classification of embedded points by regressing the closest approximation …
University of Hildesheim（希尔德斯海姆大学）；Volkswagen AG（大众汽车公司）
Recent work has shown the efficiency of deep learning models such as Fully Convolutional Networks (FCN) or Recurrent Neural Networks (RNN) to deal with Time Series Regression (TSR) problems. These models sometimes need a lot of data to be able to generalize, yet the time series are sometimes not long enough to be able to learn patterns. Therefore, it is important to make use of information across time series to improve learning. In this paper, we will explore the idea of using meta-learning for quickly adapting model parameters to new short-history time series by modifying the original idea of…
Meta-learning for sample-efficient Bayesian optimisation of fed-batch processes
Department of Computing, Imperial College London, United Kingdom（帝国理工学院伦敦分校计算机系）；BASF SE, Ludwigshafen, Germany（巴斯夫股份有限公司，德国路德维希沙芬）；School of Mathematical Sciences, Lancaster University, United Kingdom（兰卡斯特大学数学科学学院）；Department of Computer Science, University of Oxford, United Kingdom（牛津大学计算机科学系）
University of Maryland, College Park（马里兰大学帕克分校）；Microsoft（微软）
Conventional image classifiers are trained by randomly sampling mini-batches of images. To achieve state-of-the-art performance, practitioners use sophisticated data augmentation schemes to expand the amount of training data available for sampling. In contrast, meta-learning algorithms sample support data, query data, and tasks on each training step. In this complex sampling scenario, data augmentation can be used not only to expand the number of images available per class, but also to generate entirely new classes/tasks. We systematically dissect the meta-learning pipeline and investigate the…
Bosch Center for Artificial Intelligence（博世人工智能中心）
Meta-learning is widely used in few-shot classification and function regression due to its ability to quickly adapt to unseen tasks. However, it has not yet been well explored on regression tasks with high dimensional inputs such as images. This paper makes two main contributions that help understand this barely explored area. \emph{First}, we design two new types of cross-category level vision regression tasks, namely object discovery and pose estimation of unprecedented complexity in the meta-learning domain for computer vision. To this end, we (i) exhaustively evaluate common meta-learning …
Gaussian Process (GP) regression has seen widespread use in robotics due to its generality, simplicity of use, and the utility of Bayesian predictions. The predominant implementation of GP regression is a nonparameteric kernel-based approach, as it enables fitting of arbitrary nonlinear functions. However, this approach suffers from two main drawbacks: (1) it is computationally inefficient, as computation scales poorly with the number of samples; and (2) it can be data inefficient, as encoding prior knowledge that can aid the model through the choice of kernel and associated hyperparameters is…
Reproducible translation of transcriptomics data has been hampered by the ubiquitous presence of batch effects. Statistical methods for managing batch effects were initially developed in the setting of sample group comparison and later borrowed for other settings such as survival outcome prediction. The most notable such method is ComBat, which adjusts for batches by including it as a covariate alongside sample groups in a linear regression. In survival prediction, however, ComBat is used without definable groups for survival outcome and is done sequentially with survival regression for a pote…
LLM-Meta-SR: In-Context Learning for Evolving Selection Operators in Symbolic Regression
Centre for Data Science and Artificial Intelligence & School of Engineering and Computer Science, Victoria University of Wellington（惠灵顿维多利亚大学数据科学与人工智能中心及工程与计算机科学学院）；Department of Computer Science and Engineering, Michigan State University（密歇根州立大学计算机科学与工程系）
We consider the task of meta-analysis in high-dimensional settings in which the data sources are similar but non-identical. To borrow strength across such heterogeneous datasets, we introduce a global parameter that emphasizes interpretability and statistical efficiency in the presence of heterogeneity. We also propose a one-shot estimator of the global parameter that preserves the anonymity of the data sources and converges at a rate that depends on the size of the combined dataset. For high-dimensional linear model settings, we demonstrate the superiority of our identification restrictions i…
Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs to larger datasets, several sparse approximations based on so-called inducing points have been proposed in the literature. In this work we investigate the connection between a general class of sparse inducing point GP regression methods and Bayesian recursive estimation which enables Kalman Filter like updating for online learning. The majority of previous …
In this paper, we consider the meta learning problem for estimating the graphs associated with high-dimensional Ising models, using the method of $\ell_1$-regularized logistic regression for neighborhood selection of each node. Our goal is to use the information learned from the auxiliary tasks in the learning of the novel task to reduce its sufficient sample complexity. To this end, we propose a novel generative model as well as an improper estimation method. In our setting, all the tasks are \emph{similar} in their \emph{random} model parameters and supports. By pooling all the samples from …
Heriot-Watt University（赫瑞-瓦特大学）；University of Edinburgh（爱丁堡大学）；SeeByte Ltd.（SeeByte有限公司）
Meta-Learning (ML) has proven to be a useful tool for training Few-Shot Learning (FSL) algorithms by exposure to batches of tasks sampled from a meta-dataset. However, the standard training procedure overlooks the dynamic nature of the real-world where object classes are likely to occur at different frequencies. While it is generally understood that imbalanced tasks harm the performance of supervised methods, there is no significant research examining the impact of imbalanced meta-datasets on the FSL evaluation task. This study exposes the magnitude and extent of this problem. Our results show…
Bayesian Sparse Regression for Microbiome-Metabolite Data Integration
The University of Texas Health Science Center at Houston（德克萨斯大学健康科学中心休斯顿分校）；The University of Texas MD Anderson Cancer Center（德克萨斯大学安德森癌症中心）；Rice University（莱斯大学）
University of Toronto（多伦多大学）；Toronto AI Lab（多伦多人工智能实验室）；LG Electronics Canada（LG电子加拿大公司）
Dataset distillation aims to learn a small synthetic dataset that preserves most of the information from the original dataset. Dataset distillation can be formulated as a bi-level meta-learning problem where the outer loop optimizes the meta-dataset and the inner loop trains a model on the distilled data. Meta-gradient computation is one of the key challenges in this formulation, as differentiating through the inner loop learning procedure introduces significant computation and memory costs. In this paper, we address these challenges using neural Feature Regression with Pooling (FRePo), achiev…
Meta-learning optimizes the hyperparameters of a training procedure, such as its initialization, kernel, or learning rate, based on data sampled from a number of auxiliary tasks. A key underlying assumption is that the auxiliary tasks, known as meta-training tasks, share the same generating distribution as the tasks to be encountered at deployment time, known as meta-test tasks. This may, however, not be the case when the test environment differ from the meta-training conditions. To address shifts in task generating distribution between meta-training and meta-testing phases, this paper introdu…
Massachusetts Institute of Technology（麻省理工学院）；Istituto Italiano di Tecnologia（意大利理工学院）；Università degli Studi di Genova（热那亚大学）
In the setting of nonparametric regression, we propose and study a combination of stochastic gradient methods with Nyström subsampling, allowing multiple passes over the data and mini-batches. Generalization error bounds for the studied algorithm are provided. Particularly, optimal learning rates are derived considering different possible choices of the step-size, the mini-batch size, the number of iterations/passes, and the subsampling level. In comparison with state-of-the-art algorithms such as the classic stochastic gradient methods and kernel ridge regression with Nyström, the studied alg…
NEC Laboratories Europe（欧洲NEC实验室）；Josef Stefan Institute（约瑟夫·斯特凡研究所）
Ensembles are popular methods for solving practical supervised learning problems. They reduce the risk of having underperforming models in production-grade software. Although critical, methods for learning heterogeneous regression ensembles have not been proposed at large scale, whereas in classical ML literature, stacking, cascading and voting are mostly restricted to classification problems. Regression poses distinct learning challenges that may result in poor performance, even when using well established homogeneous ensemble schemas such as bagging or boosting. In this paper, we introduce M…
IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Generating high quality uncertainty estimates for sequential regression, particularly deep recurrent networks, remains a challenging and open problem. Existing approaches often make restrictive assumptions (such as stationarity) yet still perform poorly in practice, particularly in presence of real world non-stationary signals and drift. This paper describes a flexible method that can generate symmetric and asymmetric uncertainty estimates, makes no assumptions about stationarity, and outperforms competitive baselines on both drift and non drift scenarios. This work helps make sequential regre…
Pakistan Institute of Engineering and Applied Sciences (PIEAS)（巴基斯坦工程与应用科学学院（PIEAS））
Learning using privileged information (LUPI) is a powerful heterogenous feature space machine learning framework that allows a machine learning model to learn from highly informative or privileged features which are available during training only to generate test predictions using input space features which are available both during training and testing. LUPI can significantly improve prediction performance in a variety of machine learning problems. However, existing large margin and neural network implementations of learning using privileged information are mostly designed for classification …
This study presents an efficient incremental/decremental approach for big streams based on Kernel Ridge Regression (KRR), a frequently used data analysis in cloud centers. To avoid reanalyzing the whole dataset whenever sensors receive new training data, typical incremental KRR used a single-instance mechanism for updating an existing system. However, this inevitably increased redundant computational time, not to mention applicability to big streams. To this end, the proposed mechanism supports incremental/decremental processing for both single and multiple samples (i.e., batch processing). A …
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
We study generalization properties of distributed algorithms in the setting of nonparametric regression over a reproducing kernel Hilbert space (RKHS). We first investigate distributed stochastic gradient methods (SGM), with mini-batches and multi-passes over the data. We show that optimal generalization error bounds can be retained for distributed SGM provided that the partition level is not too large. We then extend our results to spectral-regularization algorithms (SRA), including kernel ridge regression (KRR), kernel principal component analysis, and gradient methods. Our results are super…
Highly Imbalanced Regression with Tabular Data in SEP and Other Applications
Department of Electrical Engineering and Computer Science（电气工程与计算机科学系）；Department of Aerospace, Physics and Space Sciences（航空航天、物理与空间科学系）；Florida Institute of Technology（佛罗里达理工学院）
Meta-learning to Calibrate Gaussian Processes with Deep Kernels for Regression Uncertainty Estimation
NTT Communication Science Laboratories, NTT Corporation（NTT集团NTT通信科学实验室）；NTT Computer and Data Science Laboratories, NTT Corporation（NTT集团NTT计算机与数据科学实验室）
To solve a machine learning problem, one typically needs to perform data preprocessing, modeling, and hyperparameter tuning, which is known as model selection and hyperparameter optimization.The goal of automated machine learning (AutoML) is to design methods that can automatically perform model selection and hyperparameter optimization without human interventions for a given dataset. In this paper, we propose a meta-learning method that can search for a high-performance machine learning pipeline from the predefined set of candidate pipelines for supervised classification datasets in an effici…
Bankura Unnayani Institue of Engineering（班库拉乌纳亚尼工程学院）
Regression analysis is an important machine learning task used for predictive analytic in business, sports analysis, etc. In regression analysis, optimization algorithms play a significant role in search the coefficients in the regression model. In this paper, nonlinear regression analysis using a recently developed meta-heuristic Multi-Verse Optimizer (MVO) is proposed. The proposed method is applied to 10 well-known benchmark nonlinear regression problems. A comparative study has been conducted with Particle Swarm Optimizer (PSO). The experimental results demonstrate that the proposed method…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Cornell University（康奈尔大学）
We demonstrate the applicability of model-agnostic algorithms for meta-learning, specifically Reptile, to GNN models in molecular regression tasks. Using meta-learning we are able to learn new chemical prediction tasks with only a few model updates, as compared to using randomly initialized GNNs which require learning each regression task from scratch. We experimentally show that GNN layer expressivity is correlated to improved meta-learning. Additionally, we also experiment with GNN emsembles which yield best performance and rapid convergence for k-shot learning.
Metabolomic data can potentially enable accurate, non-invasive and low-cost prediction of coronary artery disease. Regression-based analytical approaches however might fail to fully account for interactions between metabolites, rely on a priori selected input features and thus might suffer from poorer accuracy. Supervised machine learning methods can potentially be used in order to fully exploit the dimensionality and richness of the data. In this paper, we systematically implement and evaluate a set of supervised learning methods (L1 regression, random forest classifier) and compare them to t…
Trinity College Dublin（都柏林圣三一学院）；Maynooth University（梅努斯大学）
Understanding hand-object pose with computer vision opens the door to new applications in mixed reality, assisted living or human-robot interaction. Most methods are trained and evaluated on balanced datasets. This is of limited use in real-world applications; how do these methods perform in the wild on unknown objects? We propose a novel benchmark for object group distribution shifts in hand and object pose regression. We then test the hypothesis that meta-learning a baseline pose regression neural network can adapt to these shifts and generalize better to unknown objects. Our results show me…
From Regression to Inference: Meta-Learning Predictors for Neural Architecture Search
Department of Mathematics（数学系）；School of Mathematical and Statistical Sciences（数学与统计科学学院）；University of California, Riverside（加州大学河滨分校）；Southern Illinois University Carbondale（南伊利诺伊大学卡罗尔梅尔分校）
