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To explain complex models based on their inputs, many feature attribution methods have been developed that assign importance scores to input features. However, some recent work challenges the robustness of feature attributions by showing that these methods are sensitive to input and model perturbations, while other work addresses this robustness issue by proposing robust attribution methods and model modifications. Nevertheless, previous work on attribution robustness has focused primarily on gradient-based feature attributions. In contrast, the robustness properties of removal-based attribution methods are not comprehensively well understood. To bridge this gap, we theoretically characterize the robustness of removal-based feature attributions. Specifically, we provide a unified analysis of such methods and prove upper bounds for the difference between intact and perturbed attributions, under settings of both input and model perturbations. Our empirical experiments on synthetic and real-world data validate our theoretical results and demonstrate their practical implications.

One-shot channel simulation is a fundamental data compression problem concerned with encoding a single sample from a target distribution $Q$ using a coding distribution $P$ using as few bits as possible on average. Algorithms that solve this problem find applications in neural data compression and differential privacy and can serve as a more efficient alternative to quantization-based methods. Sadly, existing solutions are too slow or have limited applicability, preventing widespread adoption. In this paper, we conclusively solve one-shot channel simulation for one-dimensional problems where the target-proposal density ratio is unimodal by describing an algorithm with optimal runtime. We achieve this by constructing a rejection sampling procedure equivalent to greedily searching over the points of a Poisson process. Hence, we call our algorithm greedy Poisson rejection sampling (GPRS) and analyze the correctness and time complexity of several of its variants. Finally, we empirically verify our theorems, demonstrating that GPRS significantly outperforms the current state-of-the-art method, A* coding.

This study demonstrates the existence of a testable condition for the identification of the causal effect of a treatment on an outcome in observational data, which relies on two sets of variables: observed covariates to be controlled for and a suspected instrument. Under a causal structure commonly found in empirical applications, the testable conditional independence of the suspected instrument and the outcome given the treatment and the covariates has two implications. First, the instrument is valid, i.e. it does not directly affect the outcome (other than through the treatment) and is unconfounded conditional on the covariates. Second, the treatment is unconfounded conditional on the covariates such that the treatment effect is identified. We suggest tests of this conditional independence based on machine learning methods that account for covariates in a data-driven way and investigate their asymptotic behavior and finite sample performance in a simulation study. We also apply our testing approach to evaluating the impact of fertility on female labor supply when using the sibling sex ratio of the first two children as supposed instrument, which by and large points to a violation of our testable implication for the moderate set of socio-economic covariates considered.

We develop a principled approach to end-to-end learning in stochastic optimization. First, we show that the standard end-to-end learning algorithm admits a Bayesian interpretation and trains a posterior Bayes action map. Building on the insights of this analysis, we then propose new end-to-end learning algorithms for training decision maps that output solutions of empirical risk minimization and distributionally robust optimization problems, two dominant modeling paradigms in optimization under uncertainty. Numerical results for a synthetic newsvendor problem illustrate the key differences between alternative training schemes. We also investigate an economic dispatch problem based on real data to showcase the impact of the neural network architecture of the decision maps on their test performance.

In this paper, we study the estimation of the derivative of a regression function in a standard univariate regression model. The estimators are defined either by derivating nonparametric least-squares estimators of the regression function or by estimating the projection of the derivative. We prove two simple risk bounds allowing to compare our estimators. More elaborate bounds under a stability assumption are then provided. Bases and spaces on which we can illustrate our assumptions and first results are both of compact or non compact type, and we discuss the rates reached by our estimators. They turn out to be optimal in the compact case. Lastly, we propose a model selection procedure and prove the associated risk bound. To consider bases with a non compact support makes the problem difficult.

We study causal effect estimation from a mixture of observational and interventional data in a confounded linear regression model with multivariate treatments. We show that the statistical efficiency in terms of expected squared error can be improved by combining estimators arising from both the observational and interventional setting. To this end, we derive methods based on matrix weighted linear estimators and prove that our methods are asymptotically unbiased in the infinite sample limit. This is an important improvement compared to the pooled estimator using the union of interventional and observational data, for which the bias only vanishes if the ratio of observational to interventional data tends to zero. Studies on synthetic data confirm our theoretical findings. In settings where confounding is substantial and the ratio of observational to interventional data is large, our estimators outperform a Stein-type estimator and various other baselines.

Automated program repair techniques aim to aid software developers with the challenging task of fixing bugs. In heuristic-based program repair, a search space of program variants is created by applying mutation operations on the source code to find potential patches for bugs. Most commonly, every selection of a mutation operator during search is performed uniformly at random. The inefficiency of this critical step in the search creates many variants that do not compile or break intended functionality, wasting considerable resources as a result. In this paper, we address this issue and propose a reinforcement learning-based approach to optimise the selection of mutation operators in heuristic-based program repair. Our solution is programming language, granularity-level, and search strategy agnostic and allows for easy augmentation into existing heuristic-based repair tools. We conduct extensive experimentation on four operator selection techniques, two reward types, two credit assignment strategies, two integration methods, and three sets of mutation operators using 22,300 independent repair attempts. We evaluate our approach on 353 real-world bugs from the Defects4J benchmark. Results show that the epsilon-greedy multi-armed bandit algorithm with average credit assignment is best for mutation operator selection. Our approach exhibits a 17.3% improvement upon the baseline, by generating patches for 9 additional bugs for a total of 61 patched bugs in the Defects4J benchmark.

Diffusion models are a class of deep generative models that have shown impressive results on various tasks with dense theoretical founding. Although diffusion models have achieved impressive quality and diversity of sample synthesis than other state-of-the-art models, they still suffer from costly sampling procedure and sub-optimal likelihood estimation. Recent studies have shown great enthusiasm on improving the performance of diffusion model. In this article, we present a first comprehensive review of existing variants of the diffusion models. Specifically, we provide a first taxonomy of diffusion models and categorize them variants to three types, namely sampling-acceleration enhancement, likelihood-maximization enhancement and data-generalization enhancement. We also introduce in detail other five generative models (i.e., variational autoencoders, generative adversarial networks, normalizing flow, autoregressive models, and energy-based models), and clarify the connections between diffusion models and these generative models. Then we make a thorough investigation into the applications of diffusion models, including computer vision, natural language processing, waveform signal processing, multi-modal modeling, molecular graph generation, time series modeling, and adversarial purification. Furthermore, we propose new perspectives pertaining to the development of this generative model.

This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of stochastic systems affected by external manipulation (interventions). This thesis contributes to the research areas concerning the estimation of causal effects, causal structure learning, and distributionally robust (out-of-distribution generalizing) prediction methods. We present novel and consistent linear and non-linear causal effects estimators in instrumental variable settings that employ data-dependent mean squared prediction error regularization. Our proposed estimators show, in certain settings, mean squared error improvements compared to both canonical and state-of-the-art estimators. We show that recent research on distributionally robust prediction methods has connections to well-studied estimators from econometrics. This connection leads us to prove that general K-class estimators possess distributional robustness properties. We, furthermore, propose a general framework for distributional robustness with respect to intervention-induced distributions. In this framework, we derive sufficient conditions for the identifiability of distributionally robust prediction methods and present impossibility results that show the necessity of several of these conditions. We present a new structure learning method applicable in additive noise models with directed trees as causal graphs. We prove consistency in a vanishing identifiability setup and provide a method for testing substructure hypotheses with asymptotic family-wise error control that remains valid post-selection. Finally, we present heuristic ideas for learning summary graphs of nonlinear time-series models.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.