Hypothesis tests calibrated by (re)sampling methods (such as permutation, rank and bootstrap tests) are useful tools for statistical analysis, at the computational cost of requiring Monte-Carlo sampling for calibration. It is common and almost universal practice to execute such tests with predetermined and large number of Monte-Carlo samples, and disregard any randomness from this sampling at the time of drawing and reporting inference. At best, this approach leads to computational inefficiency, and at worst to invalid inference. That being said, a number of approaches in the literature have been proposed to adaptively guide analysts in choosing the number of Monte-Carlo samples, by sequentially deciding when to stop collecting samples and draw inference. These works introduce varying competing notions of what constitutes "valid" inference, complicating the landscape for analysts seeking suitable methodology. Furthermore, the majority of these approaches solely guarantee a meaningful estimate of the testing outcome, not the $p$-value itself $\unicode{x2014}$ which is insufficient for many practical applications. In this paper, we survey the relevant literature, and build bridges between the scattered validity notions, highlighting some of their complementary roles. We also introduce a new practical methodology that provides an estimate of the $p$-value of the Monte-Carlo test, endowed with practically relevant validity guarantees. Moreover, our methodology is sequential, updating the $p$-value estimate after each new Monte-Carlo sample has been drawn, while retaining important validity guarantees regardless of the selected stopping time. We conclude this paper with a set of recommendations for the practitioner, both in terms of selection of methodology and manner of reporting results.
相關內容
Worst-case fairness with off-the-shelf demographics achieves group parity by maximizing the model utility of the worst-off group. Nevertheless, demographic information is often unavailable in practical scenarios, which impedes the use of such a direct max-min formulation. Recent advances have reframed this learning problem by introducing the lower bound of minimal partition ratio, denoted as $\alpha$, as side information, referred to as ``$\alpha$-sized worst-case fairness'' in this paper. We first justify the practical significance of this setting by presenting noteworthy evidence from the data privacy perspective, which has been overlooked by existing research. Without imposing specific requirements on loss functions, we propose reweighting the training samples based on their intrinsic importance to fairness. Given the global nature of the worst-case formulation, we further develop a stochastic learning scheme to simplify the training process without compromising model performance. Additionally, we address the issue of outliers and provide a robust variant to handle potential outliers during model training. Our theoretical analysis and experimental observations reveal the connections between the proposed approaches and existing ``fairness-through-reweighting'' studies, with extensive experimental results on fairness benchmarks demonstrating the superiority of our methods.
Multi-object multi-part scene segmentation is a challenging task whose complexity scales exponentially with part granularity and number of scene objects. To address the task, we propose a plug-and-play approach termed OLAF. First, we augment the input (RGB) with channels containing object-based structural cues (fg/bg mask, boundary edge mask). We propose a weight adaptation technique which enables regular (RGB) pre-trained models to process the augmented (5-channel) input in a stable manner during optimization. In addition, we introduce an encoder module termed LDF to provide low-level dense feature guidance. This assists segmentation, particularly for smaller parts. OLAF enables significant mIoU gains of $\mathbf{3.3}$ (Pascal-Parts-58), $\mathbf{3.5}$ (Pascal-Parts-108) over the SOTA model. On the most challenging variant (Pascal-Parts-201), the gain is $\mathbf{4.0}$. Experimentally, we show that OLAF's broad applicability enables gains across multiple architectures (CNN, U-Net, Transformer) and datasets. The code is available at olafseg.github.io
A non-uniform implicit-explicit L1 mixed finite element method (IMEX-L1-MFEM) is investigated for a class of time-fractional partial integro-differential equations (PIDEs) with space-time dependent coefficients and non-self-adjoint elliptic part. The proposed fully discrete method combines an IMEX-L1 method on a graded mesh in the temporal variable with a mixed finite element method in spatial variables. The focus of the study is to analyze stability results and to establish optimal error estimates, up to a logarithmic factor, for both the solution and the flux in $L^2$-norm when the initial data $u_0\in H_0^1(\Omega)\cap H^2(\Omega)$. Additionally, an error estimate in $L^\infty$-norm is derived for 2D problems. All the derived estimates and bounds in this article remain valid as $\alpha\to 1^{-}$, where $\alpha$ is the order of the Caputo fractional derivative. Finally, the results of several numerical experiments conducted at the end of this paper are confirming our theoretical findings.
Generative modelling paradigms based on denoising diffusion processes have emerged as a leading candidate for conditional sampling in inverse problems. In many real-world applications, we often have access to large, expensively trained unconditional diffusion models, which we aim to exploit for improving conditional sampling. Most recent approaches are motivated heuristically and lack a unifying framework, obscuring connections between them. Further, they often suffer from issues such as being very sensitive to hyperparameters, being expensive to train or needing access to weights hidden behind a closed API. In this work, we unify conditional training and sampling using the mathematically well-understood Doob's h-transform. This new perspective allows us to unify many existing methods under a common umbrella. Under this framework, we propose DEFT (Doob's h-transform Efficient FineTuning), a new approach for conditional generation that simply fine-tunes a very small network to quickly learn the conditional $h$-transform, while keeping the larger unconditional network unchanged. DEFT is much faster than existing baselines while achieving state-of-the-art performance across a variety of linear and non-linear benchmarks. On image reconstruction tasks, we achieve speedups of up to 1.6$\times$, while having the best perceptual quality on natural images and reconstruction performance on medical images. Further, we also provide initial experiments on protein motif scaffolding and outperform reconstruction guidance methods.
Robot learning holds tremendous promise to unlock the full potential of flexible, general, and dexterous robot systems, as well as to address some of the deepest questions in artificial intelligence. However, bringing robot learning to the level of generality required for effective real-world systems faces major obstacles in terms of data, generalization, and robustness. In this paper, we discuss how generalist robot policies (i.e., robot foundation models) can address these challenges, and how we can design effective generalist robot policies for complex and highly dexterous tasks. We propose a novel flow matching architecture built on top of a pre-trained vision-language model (VLM) to inherit Internet-scale semantic knowledge. We then discuss how this model can be trained on a large and diverse dataset from multiple dexterous robot platforms, including single-arm robots, dual-arm robots, and mobile manipulators. We evaluate our model in terms of its ability to perform tasks in zero shot after pre-training, follow language instructions from people and from a high-level VLM policy, and its ability to acquire new skills via fine-tuning. Our results cover a wide variety of tasks, such as laundry folding, table cleaning, and assembling boxes.
The fairness of clustering algorithms has gained widespread attention across various areas, including machine learning, In this paper, we study fair $k$-means clustering in Euclidean space. Given a dataset comprising several groups, the fairness constraint requires that each cluster should contain a proportion of points from each group within specified lower and upper bounds. Due to these fairness constraints, determining the optimal locations of $k$ centers is a quite challenging task. We propose a novel ``Relax and Merge'' framework that returns a $(1+4\rho + O(\epsilon))$-approximate solution, where $\rho$ is the approximate ratio of an off-the-shelf vanilla $k$-means algorithm and $O(\epsilon)$ can be an arbitrarily small positive number. If equipped with a PTAS of $k$-means, our solution can achieve an approximation ratio of $(5+O(\epsilon))$ with only a slight violation of the fairness constraints, which improves the current state-of-the-art approximation guarantee. Furthermore, using our framework, we can also obtain a $(1+4\rho +O(\epsilon))$-approximate solution for the $k$-sparse Wasserstein Barycenter problem, which is a fundamental optimization problem in the field of optimal transport, and a $(2+6\rho)$-approximate solution for the strictly fair $k$-means clustering with no violation, both of which are better than the current state-of-the-art methods. In addition, the empirical results demonstrate that our proposed algorithm can significantly outperform baseline approaches in terms of clustering cost.
We investigate popular resampling methods for estimating the uncertainty of statistical models, such as subsampling, bootstrap and the jackknife, and their performance in high-dimensional supervised regression tasks. We provide a tight asymptotic description of the biases and variances estimated by these methods in the context of generalized linear models, such as ridge and logistic regression, taking the limit where the number of samples $n$ and dimension $d$ of the covariates grow at a comparable fixed rate $\alpha\!=\! n/d$. Our findings are three-fold: i) resampling methods are fraught with problems in high dimensions and exhibit the double-descent-like behavior typical of these situations; ii) only when $\alpha$ is large enough do they provide consistent and reliable error estimations (we give convergence rates); iii) in the over-parametrized regime $\alpha\!<\!1$ relevant to modern machine learning practice, their predictions are not consistent, even with optimal regularization.
This paper employs a localized orthogonal decomposition (LOD) method with $H^1$ interpolation for solving the multiscale elliptic problem. This method does not need any assumptions on scale separation. We give a priori error estimate for the proposed method. The theoretical results are conformed by various numerical experiments.
Graph convolution networks (GCN) are increasingly popular in many applications, yet remain notoriously hard to train over large graph datasets. They need to compute node representations recursively from their neighbors. Current GCN training algorithms suffer from either high computational costs that grow exponentially with the number of layers, or high memory usage for loading the entire graph and node embeddings. In this paper, we propose a novel efficient layer-wise training framework for GCN (L-GCN), that disentangles feature aggregation and feature transformation during training, hence greatly reducing time and memory complexities. We present theoretical analysis for L-GCN under the graph isomorphism framework, that L-GCN leads to as powerful GCNs as the more costly conventional training algorithm does, under mild conditions. We further propose L^2-GCN, which learns a controller for each layer that can automatically adjust the training epochs per layer in L-GCN. Experiments show that L-GCN is faster than state-of-the-arts by at least an order of magnitude, with a consistent of memory usage not dependent on dataset size, while maintaining comparable prediction performance. With the learned controller, L^2-GCN can further cut the training time in half. Our codes are available at //github.com/Shen-Lab/L2-GCN.
When labeled training data is scarce, a promising data augmentation approach is to generate visual features of unknown classes using their attributes. To learn the class conditional distribution of CNN features, these models rely on pairs of image features and class attributes. Hence, they can not make use of the abundance of unlabeled data samples. In this paper, we tackle any-shot learning problems i.e. zero-shot and few-shot, in a unified feature generating framework that operates in both inductive and transductive learning settings. We develop a conditional generative model that combines the strength of VAE and GANs and in addition, via an unconditional discriminator, learns the marginal feature distribution of unlabeled images. We empirically show that our model learns highly discriminative CNN features for five datasets, i.e. CUB, SUN, AWA and ImageNet, and establish a new state-of-the-art in any-shot learning, i.e. inductive and transductive (generalized) zero- and few-shot learning settings. We also demonstrate that our learned features are interpretable: we visualize them by inverting them back to the pixel space and we explain them by generating textual arguments of why they are associated with a certain label.
小貼士
登錄享
相關主題
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191