The Distributional Random Forest (DRF) is a recently introduced Random Forest algorithm to estimate multivariate conditional distributions. Due to its general estimation procedure, it can be employed to estimate a wide range of targets such as conditional average treatment effects, conditional quantiles, and conditional correlations. However, only results about the consistency and convergence rate of the DRF prediction are available so far. We characterize the asymptotic distribution of DRF and develop a bootstrap approximation of it. This allows us to derive inferential tools for quantifying standard errors and the construction of confidence regions that have asymptotic coverage guarantees. In simulation studies, we empirically validate the developed theory for inference of low-dimensional targets and for testing distributional differences between two populations.
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Confidence intervals based on the central limit theorem (CLT) are a cornerstone of classical statistics. Despite being only asymptotically valid, they are ubiquitous because they permit statistical inference under very weak assumptions, and can often be applied to problems even when nonasymptotic inference is impossible. This paper introduces time-uniform analogues of such asymptotic confidence intervals. To elaborate, our methods take the form of confidence sequences (CS) -- sequences of confidence intervals that are uniformly valid over time. CSs provide valid inference at arbitrary stopping times, incurring no penalties for "peeking" at the data, unlike classical confidence intervals which require the sample size to be fixed in advance. Existing CSs in the literature are nonasymptotic, and hence do not enjoy the aforementioned broad applicability of asymptotic confidence intervals. Our work bridges the gap by giving a definition for "asymptotic CSs", and deriving a universal asymptotic CS that requires only weak CLT-like assumptions. While the CLT approximates the distribution of a sample average by that of a Gaussian at a fixed sample size, we use strong invariance principles (stemming from the seminal 1960s work of Strassen and improvements by Koml\'os, Major, and Tusn\'ady) to uniformly approximate the entire sample average process by an implicit Gaussian process. We demonstrate their utility by deriving nonparametric asymptotic CSs for the average treatment effect based on doubly robust estimators in observational studies, for which no nonasymptotic methods can exist even in the fixed-time regime. This enables causal inference that can be continuously monitored and adaptively stopped.
A block Markov chain is a Markov chain whose state space can be partitioned into a finite number of clusters such that the transition probabilities only depend on the clusters. Block Markov chains thus serve as a model for Markov chains with communities. This paper establishes limiting laws for the singular value distributions of the empirical transition matrix and empirical frequency matrix associated to a sample path of the block Markov chain whenever the length of the sample path is $\Theta(n^2)$ with $n$ the size of the state space. The proof approach is split into two parts. First, we introduce a class of symmetric random matrices with dependent entries called approximately uncorrelated random matrices with variance profile. We establish their limiting eigenvalue distributions by means of the moment method. Second, we develop a coupling argument to show that this general-purpose result applies to the singular value distributions associated with the block Markov chain.
Classic Machine Learning techniques require training on data available in a single data lake. However, aggregating data from different owners is not always convenient for different reasons, including security, privacy and secrecy. Data carry a value that might vanish when shared with others; the ability to avoid sharing the data enables industrial applications where security and privacy are of paramount importance, making it possible to train global models by implementing only local policies which can be run independently and even on air-gapped data centres. Federated Learning (FL) is a distributed machine learning approach which has emerged as an effective way to address privacy concerns by only sharing local AI models while keeping the data decentralized. Two critical challenges of Federated Learning are managing the heterogeneous systems in the same federated network and dealing with real data, which are often not independently and identically distributed (non-IID) among the clients. In this paper, we focus on the second problem, i.e., the problem of statistical heterogeneity of the data in the same federated network. In this setting, local models might be strayed far from the local optimum of the complete dataset, thus possibly hindering the convergence of the federated model. Several Federated Learning algorithms, such as FedAvg, FedProx and Federated Curvature (FedCurv), aiming at tackling the non-IID setting, have already been proposed. This work provides an empirical assessment of the behaviour of FedAvg and FedCurv in common non-IID scenarios. Results show that the number of epochs per round is an important hyper-parameter that, when tuned appropriately, can lead to significant performance gains while reducing the communication cost. As a side product of this work, we release the non-IID version of the datasets we used so to facilitate further comparisons from the FL community.
Conventional de-noising methods rely on the assumption that all samples are independent and identically distributed, so the resultant classifier, though disturbed by noise, can still easily identify the noises as the outliers of training distribution. However, the assumption is unrealistic in large-scale data that is inevitably long-tailed. Such imbalanced training data makes a classifier less discriminative for the tail classes, whose previously "easy" noises are now turned into "hard" ones -- they are almost as outliers as the clean tail samples. We introduce this new challenge as Noisy Long-Tailed Classification (NLT). Not surprisingly, we find that most de-noising methods fail to identify the hard noises, resulting in significant performance drop on the three proposed NLT benchmarks: ImageNet-NLT, Animal10-NLT, and Food101-NLT. To this end, we design an iterative noisy learning framework called Hard-to-Easy (H2E). Our bootstrapping philosophy is to first learn a classifier as noise identifier invariant to the class and context distributional changes, reducing "hard" noises to "easy" ones, whose removal further improves the invariance. Experimental results show that our H2E outperforms state-of-the-art de-noising methods and their ablations on long-tailed settings while maintaining a stable performance on the conventional balanced settings. Datasets and codes are available at //github.com/yxymessi/H2E-Framework
Out-Of-Distribution generalization (OOD) is all about learning invariance against environmental changes. If the context in every class is evenly distributed, OOD would be trivial because the context can be easily removed due to an underlying principle: class is invariant to context. However, collecting such a balanced dataset is impractical. Learning on imbalanced data makes the model bias to context and thus hurts OOD. Therefore, the key to OOD is context balance. We argue that the widely adopted assumption in prior work, the context bias can be directly annotated or estimated from biased class prediction, renders the context incomplete or even incorrect. In contrast, we point out the everoverlooked other side of the above principle: context is also invariant to class, which motivates us to consider the classes (which are already labeled) as the varying environments to resolve context bias (without context labels). We implement this idea by minimizing the contrastive loss of intra-class sample similarity while assuring this similarity to be invariant across all classes. On benchmarks with various context biases and domain gaps, we show that a simple re-weighting based classifier equipped with our context estimation achieves state-of-the-art performance. We provide the theoretical justifications in Appendix and codes on //github.com/simpleshinobu/IRMCon.
The variety of complex algorithmic approaches for tackling time-series classification problems has grown considerably over the past decades, including the development of sophisticated but challenging-to-interpret deep-learning-based methods. But without comparison to simpler methods it can be difficult to determine when such complexity is required to obtain strong performance on a given problem. Here we evaluate the performance of an extremely simple classification approach -- a linear classifier in the space of two simple features that ignore the sequential ordering of the data: the mean and standard deviation of time-series values. Across a large repository of 128 univariate time-series classification problems, this simple distributional moment-based approach outperformed chance on 69 problems, and reached 100% accuracy on two problems. With a neuroimaging time-series case study, we find that a simple linear model based on the mean and standard deviation performs better at classifying individuals with schizophrenia than a model that additionally includes features of the time-series dynamics. Comparing the performance of simple distributional features of a time series provides important context for interpreting the performance of complex time-series classification models, which may not always be required to obtain high accuracy.
The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.
In recent years, Face Image Quality Assessment (FIQA) has become an indispensable part of the face recognition system to guarantee the stability and reliability of recognition performance in an unconstrained scenario. For this purpose, the FIQA method should consider both the intrinsic property and the recognizability of the face image. Most previous works aim to estimate the sample-wise embedding uncertainty or pair-wise similarity as the quality score, which only considers the information from partial intra-class. However, these methods ignore the valuable information from the inter-class, which is for estimating to the recognizability of face image. In this work, we argue that a high-quality face image should be similar to its intra-class samples and dissimilar to its inter-class samples. Thus, we propose a novel unsupervised FIQA method that incorporates Similarity Distribution Distance for Face Image Quality Assessment (SDD-FIQA). Our method generates quality pseudo-labels by calculating the Wasserstein Distance (WD) between the intra-class similarity distributions and inter-class similarity distributions. With these quality pseudo-labels, we are capable of training a regression network for quality prediction. Extensive experiments on benchmark datasets demonstrate that the proposed SDD-FIQA surpasses the state-of-the-arts by an impressive margin. Meanwhile, our method shows good generalization across different recognition systems.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.
Ensembles over neural network weights trained from different random initialization, known as deep ensembles, achieve state-of-the-art accuracy and calibration. The recently introduced batch ensembles provide a drop-in replacement that is more parameter efficient. In this paper, we design ensembles not only over weights, but over hyperparameters to improve the state of the art in both settings. For best performance independent of budget, we propose hyper-deep ensembles, a simple procedure that involves a random search over different hyperparameters, themselves stratified across multiple random initializations. Its strong performance highlights the benefit of combining models with both weight and hyperparameter diversity. We further propose a parameter efficient version, hyper-batch ensembles, which builds on the layer structure of batch ensembles and self-tuning networks. The computational and memory costs of our method are notably lower than typical ensembles. On image classification tasks, with MLP, LeNet, and Wide ResNet 28-10 architectures, our methodology improves upon both deep and batch ensembles.
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