Ensuring that analyses performed on a dataset are representative of the entire population is one of the central problems in statistics. Most classical techniques assume that the dataset is independent of the analyst's query and break down in the common setting where a dataset is reused for multiple, adaptively chosen, queries. This problem of \emph{adaptive data analysis} was formalized in the seminal works of Dwork et al. (STOC, 2015) and Hardt and Ullman (FOCS, 2014). We identify a remarkably simple set of assumptions under which the queries will continue to be representative even when chosen adaptively: The only requirements are that each query takes as input a random subsample and outputs few bits. This result shows that the noise inherent in subsampling is sufficient to guarantee that query responses generalize. The simplicity of this subsampling-based framework allows it to model a variety of real-world scenarios not covered by prior work. In addition to its simplicity, we demonstrate the utility of this framework by designing mechanisms for two foundational tasks, statistical queries and median finding. In particular, our mechanism for answering the broadly applicable class of statistical queries is both extremely simple and state of the art in many parameter regimes.
相關內容
Adhesive joints are increasingly used in industry for a wide variety of applications because of their favorable characteristics such as high strength-to-weight ratio, design flexibility, limited stress concentrations, planar force transfer, good damage tolerance, and fatigue resistance. Finding the optimal process parameters for an adhesive bonding process is challenging: the optimization is inherently multi-objective (aiming to maximize break strength while minimizing cost), constrained (the process should not result in any visual damage to the materials, and stress tests should not result in failures that are adhesion-related), and uncertain (testing the same process parameters several times may lead to different break strengths). Real-life physical experiments in the lab are expensive to perform. Traditional evolutionary approaches (such as genetic algorithms) are then ill-suited to solve the problem, due to the prohibitive amount of experiments required for evaluation. Although Bayesian optimization-based algorithms are preferred to solve such expensive problems, few methods consider the optimization of more than one (noisy) objective and several constraints at the same time. In this research, we successfully applied specific machine learning techniques (Gaussian Process Regression) to emulate the objective and constraint functions based on a limited amount of experimental data. The techniques are embedded in a Bayesian optimization algorithm, which succeeds in detecting Pareto-optimal process settings in a highly efficient way (i.e., requiring a limited number of physical experiments).
In this paper, we present a contraction-guided adaptive partitioning algorithm for improving interval-valued robust reachable set estimates in a nonlinear feedback loop with a neural network controller and disturbances. Based on an estimate of the contraction rate of over-approximated intervals, the algorithm chooses when and where to partition. Then, by leveraging a decoupling of the neural network verification step and reachability partitioning layers, the algorithm can provide accuracy improvements for little computational cost. This approach is applicable with any sufficiently accurate open-loop interval-valued reachability estimation technique and any method for bounding the input-output behavior of a neural network. Using contraction-based robustness analysis, we provide guarantees of the algorithm's performance with mixed monotone reachability. Finally, we demonstrate the algorithm's performance through several numerical simulations and compare it with existing methods in the literature. In particular, we report a sizable improvement in the accuracy of reachable set estimation in a fraction of the runtime as compared to state-of-the-art methods.
With the recent study of deep learning in scientific computation, the Physics-Informed Neural Networks (PINNs) method has drawn widespread attention for solving Partial Differential Equations (PDEs). Compared to traditional methods, PINNs can efficiently handle high-dimensional problems, but the accuracy is relatively low, especially for highly irregular problems. Inspired by the idea of adaptive finite element methods and incremental learning, we propose GAS, a Gaussian mixture distribution-based adaptive sampling method for PINNs. During the training procedure, GAS uses the current residual information to generate a Gaussian mixture distribution for the sampling of additional points, which are then trained together with historical data to speed up the convergence of the loss and achieve higher accuracy. Several numerical simulations on 2D and 10D problems show that GAS is a promising method that achieves state-of-the-art accuracy among deep solvers, while being comparable with traditional numerical solvers.
Problems with solutions represented by permutations are very prominent in combinatorial optimization. Thus, in recent decades, a number of evolutionary algorithms have been proposed to solve them, and among them, those based on probability models have received much attention. In that sense, most efforts have focused on introducing algorithms that are suited for solving ordering/ranking nature problems. However, when it comes to proposing probability-based evolutionary algorithms for assignment problems, the works have not gone beyond proposing simple and in most cases univariate models. In this paper, we explore the use of Doubly Stochastic Matrices (DSM) for optimizing matching and assignment nature permutation problems. To that end, we explore some learning and sampling methods to efficiently incorporate DSMs within the picture of evolutionary algorithms. Specifically, we adopt the framework of estimation of distribution algorithms and compare DSMs to some existing proposals for permutation problems. Conducted preliminary experiments on instances of the quadratic assignment problem validate this line of research and show that DSMs may obtain very competitive results, while computational cost issues still need to be further investigated.
In computer vision, contrastive learning is the most advanced unsupervised learning framework. Yet most previous methods simply apply fixed composition of data augmentations to improve data efficiency, which ignores the changes in their optimal settings over training. Thus, the pre-determined parameters of augmentation operations cannot always fit well with an evolving network during the whole training period, which degrades the quality of the learned representations. In this work, we propose AdDA, which implements a closed-loop feedback structure to a generic contrastive learning network. AdDA works by allowing the network to adaptively adjust the augmentation compositions according to the real-time feedback. This online adjustment helps maintain the dynamic optimal composition and enables the network to acquire more generalizable representations with minimal computational overhead. AdDA achieves competitive results under the common linear protocol on ImageNet-100 classification (+1.11% on MoCo v2).
The success of large language models (LLMs), like GPT-3 and ChatGPT, has led to the development of numerous cost-effective and accessible alternatives that are created by fine-tuning open-access LLMs with task-specific data (e.g., ChatDoctor) or instruction data (e.g., Alpaca). Among the various fine-tuning methods, adapter-based parameter-efficient fine-tuning (PEFT) is undoubtedly one of the most attractive topics, as it only requires fine-tuning a few external parameters instead of the entire LLMs while achieving comparable or even better performance. To enable further research on PEFT methods of LLMs, this paper presents LLM-Adapters, an easy-to-use framework that integrates various adapters into LLMs and can execute these adapter-based PEFT methods of LLMs for different tasks. The framework includes state-of-the-art open-access LLMs such as LLaMA, BLOOM, OPT, and GPT-J, as well as widely used adapters such as Series adapter, Parallel adapter, and LoRA. The framework is designed to be research-friendly, efficient, modular, and extendable, allowing the integration of new adapters and the evaluation of them with new and larger-scale LLMs. Furthermore, to evaluate the effectiveness of adapters in LLMs-Adapters, we conduct experiments on six math reasoning datasets. The results demonstrate that using adapter-based PEFT in smaller-scale LLMs (7B) with few extra trainable parameters yields comparable, and in some cases superior, performance to that of powerful LLMs (175B) in zero-shot inference on simple math reasoning datasets. Overall, we provide a promising framework for fine-tuning large LLMs on downstream tasks. We believe the proposed LLMs-Adapters will advance adapter-based PEFT research, facilitate the deployment of research pipelines, and enable practical applications to real-world systems.
In this paper, we propose double machine learning procedures to estimate genetic relatedness between two traits in a model-free framework. Most existing methods require specifying certain parametric models involving the traits and genetic variants. However, the bias due to model mis-specification may yield misleading statistical results. Moreover, the semiparametric efficient bounds for estimators of genetic relatedness are still lacking. In this paper, we develop semi-parametric efficient and model-free estimators and construct valid confidence intervals for two important measures of genetic relatedness: genetic covariance and genetic correlation, allowing both continuous and discrete responses. Based on the derived efficient influence functions of genetic relatedness, we propose a consistent estimator of the genetic covariance as long as one of genetic values is consistently estimated. The data of two traits may be collected from the same group or different groups of individuals. Various numerical studies are performed to illustrate our introduced procedures. We also apply proposed procedures to analyze Carworth Farms White mice genome-wide association study data.
This paper takes into account the estimation for the two unknown parameters of the Chen distribution with bathtub-shape hazard rate function under the improved adaptive Type-II progressive censored data. Maximum likelihood estimation for two parameters are proposed and the approximate confidence intervals are established using the asymptotic normality. Bayesian estimation are obtained under the symmetric and asymmetric loss function, during which the importance sampling and Metropolis-Hastings algorithm are proposed. Finally, the performance of various estimation methods is evaluated by Monte Carlo simulation experiments, and the proposed estimation method is illustrated through the analysis of a real data set.
In semi-supervised domain adaptation, a few labeled samples per class in the target domain guide features of the remaining target samples to aggregate around them. However, the trained model cannot produce a highly discriminative feature representation for the target domain because the training data is dominated by labeled samples from the source domain. This could lead to disconnection between the labeled and unlabeled target samples as well as misalignment between unlabeled target samples and the source domain. In this paper, we propose a novel approach called Cross-domain Adaptive Clustering to address this problem. To achieve both inter-domain and intra-domain adaptation, we first introduce an adversarial adaptive clustering loss to group features of unlabeled target data into clusters and perform cluster-wise feature alignment across the source and target domains. We further apply pseudo labeling to unlabeled samples in the target domain and retain pseudo-labels with high confidence. Pseudo labeling expands the number of ``labeled" samples in each class in the target domain, and thus produces a more robust and powerful cluster core for each class to facilitate adversarial learning. Extensive experiments on benchmark datasets, including DomainNet, Office-Home and Office, demonstrate that our proposed approach achieves the state-of-the-art performance in semi-supervised domain adaptation.
While recent studies on semi-supervised learning have shown remarkable progress in leveraging both labeled and unlabeled data, most of them presume a basic setting of the model is randomly initialized. In this work, we consider semi-supervised learning and transfer learning jointly, leading to a more practical and competitive paradigm that can utilize both powerful pre-trained models from source domain as well as labeled/unlabeled data in the target domain. To better exploit the value of both pre-trained weights and unlabeled target examples, we introduce adaptive consistency regularization that consists of two complementary components: Adaptive Knowledge Consistency (AKC) on the examples between the source and target model, and Adaptive Representation Consistency (ARC) on the target model between labeled and unlabeled examples. Examples involved in the consistency regularization are adaptively selected according to their potential contributions to the target task. We conduct extensive experiments on several popular benchmarks including CUB-200-2011, MIT Indoor-67, MURA, by fine-tuning the ImageNet pre-trained ResNet-50 model. Results show that our proposed adaptive consistency regularization outperforms state-of-the-art semi-supervised learning techniques such as Pseudo Label, Mean Teacher, and MixMatch. Moreover, our algorithm is orthogonal to existing methods and thus able to gain additional improvements on top of MixMatch and FixMatch. Our code is available at //github.com/SHI-Labs/Semi-Supervised-Transfer-Learning.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191