Even though Weighted Lasso regression has appealing statistical guarantees, it is typically avoided due to its complex search space described with thousands of hyperparameters. On the other hand, the latest progress with high-dimensional HPO methods for black-box functions demonstrates that high-dimensional applications can indeed be efficiently optimized. Despite this initial success, the high-dimensional HPO approaches are typically applied to synthetic problems with a moderate number of dimensions which limits its impact in scientific and engineering applications. To address this limitation, we propose LassoBench, a new benchmark suite tailored for an important open research topic in the Lasso community that is Weighted Lasso regression. LassoBench consists of benchmarks on both well-controlled synthetic setups (number of samples, SNR, ambient and effective dimensionalities, and multiple fidelities) and real-world datasets, which enable the use of many flavors of HPO algorithms to be improved and extended to the high-dimensional setting. We evaluate 5 state-of-the-art HPO methods and 3 baselines, and demonstrate that Bayesian optimization, in particular, can improve over the methods commonly used for sparse regression while highlighting limitations of these frameworks in very high-dimensions. Remarkably, Bayesian optimization improve the Lasso baselines on 60, 100, 300, and 1000 dimensional problems by 45.7%, 19.2%, 19.7% and 15.5%, respectively.
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Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated guarantees is uniformity, i.e., recovery succeeds for an entire class of structured signals with a fixed measurement ensemble. However, despite significant results in various special cases, a general understanding of uniform recovery from non-linear observations is still missing. This paper develops a unified approach to this problem under the assumption of i.i.d. sub-Gaussian measurement vectors. Our main result shows that a simple least-squares estimator with any convex constraint can serve as a universal recovery strategy, which is outlier robust and does not require explicit knowledge of the underlying non-linearity. Based on empirical process theory, a key technical novelty is an approximative increment condition that can be implemented for all common types of non-linear models. This flexibility allows us to apply our approach to a variety of problems in non-linear compressed sensing and high-dimensional statistics, leading to several new and improved guarantees. Each of these applications is accompanied by a conceptually simple and systematic proof, which does not rely on any deeper properties of the observation model. On the other hand, known local stability properties can be incorporated into our framework in a plug-and-play manner, thereby implying near-optimal error bounds.
When the data are sparse, optimization of hyperparameters of the kernel in Gaussian process regression by the commonly used maximum likelihood estimation (MLE) criterion often leads to overfitting. We show that choosing hyperparameters (in this case, kernel length parameter and regularization parameter) based on a criterion of the completeness of the basis in the corresponding linear regression problem is superior to MLE. We show that this is facilitated by the use of high-dimensional model representation (HDMR) whereby a low-order HDMR representation can provide reliable reference functions and large synthetic test data sets needed for basis parameter optimization even when the original data are few.
This paper presents and characterizes an Open Application Repository for Federated Learning (OARF), a benchmark suite for federated machine learning systems. Previously available benchmarks for federated learning have focused mainly on synthetic datasets and use a limited number of applications. OARF mimics more realistic application scenarios with publicly available data sets as different data silos in image, text and structured data. Our characterization shows that the benchmark suite is diverse in data size, distribution, feature distribution and learning task complexity. The extensive evaluations with reference implementations show the future research opportunities for important aspects of federated learning systems. We have developed reference implementations, and evaluated the important aspects of federated learning, including model accuracy, communication cost, throughput and convergence time. Through these evaluations, we discovered some interesting findings such as federated learning can effectively increase end-to-end throughput.
Domain classification is the fundamental task in natural language understanding (NLU), which often requires fast accommodation to new emerging domains. This constraint makes it impossible to retrain all previous domains, even if they are accessible to the new model. Most existing continual learning approaches suffer from low accuracy and performance fluctuation, especially when the distributions of old and new data are significantly different. In fact, the key real-world problem is not the absence of old data, but the inefficiency to retrain the model with the whole old dataset. Is it potential to utilize some old data to yield high accuracy and maintain stable performance, while at the same time, without introducing extra hyperparameters? In this paper, we proposed a hyperparameter-free continual learning model for text data that can stably produce high performance under various environments. Specifically, we utilize Fisher information to select exemplars that can "record" key information of the original model. Also, a novel scheme called dynamical weight consolidation is proposed to enable hyperparameter-free learning during the retrain process. Extensive experiments demonstrate that baselines suffer from fluctuated performance and therefore useless in practice. On the contrary, our proposed model CCFI significantly and consistently outperforms the best state-of-the-art method by up to 20% in average accuracy, and each component of CCFI contributes effectively to overall performance.
In this paper, we show that the diagonal of a high-dimensional sample covariance matrix stemming from $n$ independent observations of a $p$-dimensional time series with finite fourth moments can be approximated in spectral norm by the diagonal of the population covariance matrix. We assume that $n,p\to \infty$ with $p/n$ tending to a constant which might be positive or zero. As applications, we provide an approximation of the sample correlation matrix ${\mathbf R}$ and derive a variety of results for its eigenvalues. We identify the limiting spectral distribution of ${\mathbf R}$ and construct an estimator for the population correlation matrix and its eigenvalues. Finally, the almost sure limits of the extreme eigenvalues of ${\mathbf R}$ in a generalized spiked correlation model are analyzed.
Centralized Training for Decentralized Execution, where training is done in a centralized offline fashion, has become a popular solution paradigm in Multi-Agent Reinforcement Learning. Many such methods take the form of actor-critic with state-based critics, since centralized training allows access to the true system state, which can be useful during training despite not being available at execution time. State-based critics have become a common empirical choice, albeit one which has had limited theoretical justification or analysis. In this paper, we show that state-based critics can introduce bias in the policy gradient estimates, potentially undermining the asymptotic guarantees of the algorithm. We also show that, even if the state-based critics do not introduce any bias, they can still result in a larger gradient variance, contrary to the common intuition. Finally, we show the effects of the theories in practice by comparing different forms of centralized critics on a wide range of common benchmarks, and detail how various environmental properties are related to the effectiveness of different types of critics.
Approaches based on deep neural networks have achieved striking performance when testing data and training data share similar distribution, but can significantly fail otherwise. Therefore, eliminating the impact of distribution shifts between training and testing data is crucial for building performance-promising deep models. Conventional methods assume either the known heterogeneity of training data (e.g. domain labels) or the approximately equal capacities of different domains. In this paper, we consider a more challenging case where neither of the above assumptions holds. We propose to address this problem by removing the dependencies between features via learning weights for training samples, which helps deep models get rid of spurious correlations and, in turn, concentrate more on the true connection between discriminative features and labels. Extensive experiments clearly demonstrate the effectiveness of our method on multiple distribution generalization benchmarks compared with state-of-the-art counterparts. Through extensive experiments on distribution generalization benchmarks including PACS, VLCS, MNIST-M, and NICO, we show the effectiveness of our method compared with state-of-the-art counterparts.
Clustering is one of the most fundamental and wide-spread techniques in exploratory data analysis. Yet, the basic approach to clustering has not really changed: a practitioner hand-picks a task-specific clustering loss to optimize and fit the given data to reveal the underlying cluster structure. Some types of losses---such as k-means, or its non-linear version: kernelized k-means (centroid based), and DBSCAN (density based)---are popular choices due to their good empirical performance on a range of applications. Although every so often the clustering output using these standard losses fails to reveal the underlying structure, and the practitioner has to custom-design their own variation. In this work we take an intrinsically different approach to clustering: rather than fitting a dataset to a specific clustering loss, we train a recurrent model that learns how to cluster. The model uses as training pairs examples of datasets (as input) and its corresponding cluster identities (as output). By providing multiple types of training datasets as inputs, our model has the ability to generalize well on unseen datasets (new clustering tasks). Our experiments reveal that by training on simple synthetically generated datasets or on existing real datasets, we can achieve better clustering performance on unseen real-world datasets when compared with standard benchmark clustering techniques. Our meta clustering model works well even for small datasets where the usual deep learning models tend to perform worse.
Person re-identification (re-id) is a critical problem in video analytics applications such as security and surveillance. The public release of several datasets and code for vision algorithms has facilitated rapid progress in this area over the last few years. However, directly comparing re-id algorithms reported in the literature has become difficult since a wide variety of features, experimental protocols, and evaluation metrics are employed. In order to address this need, we present an extensive review and performance evaluation of single- and multi-shot re-id algorithms. The experimental protocol incorporates the most recent advances in both feature extraction and metric learning. To ensure a fair comparison, all of the approaches were implemented using a unified code library that includes 11 feature extraction algorithms and 22 metric learning and ranking techniques. All approaches were evaluated using a new large-scale dataset that closely mimics a real-world problem setting, in addition to 16 other publicly available datasets: VIPeR, GRID, CAVIAR, DukeMTMC4ReID, 3DPeS, PRID, V47, WARD, SAIVT-SoftBio, CUHK01, CHUK02, CUHK03, RAiD, iLIDSVID, HDA+ and Market1501. The evaluation codebase and results will be made publicly available for community use.
Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in theoretical computer science has shown that, in appropriate distributional models, it is possible to robustly estimate the mean and covariance with polynomial time algorithms that can tolerate a constant fraction of corruptions, independent of the dimension. However, the sample and time complexity of these algorithms is prohibitively large for high-dimensional applications. In this work, we address both of these issues by establishing sample complexity bounds that are optimal, up to logarithmic factors, as well as giving various refinements that allow the algorithms to tolerate a much larger fraction of corruptions. Finally, we show on both synthetic and real data that our algorithms have state-of-the-art performance and suddenly make high-dimensional robust estimation a realistic possibility.
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