亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

The causal capabilities of large language models (LLMs) is a matter of significant debate, with critical implications for the use of LLMs in societally impactful domains such as medicine, science, law, and policy. We further our understanding of LLMs and their causal implications, considering the distinctions between different types of causal reasoning tasks, as well as the entangled threats of construct and measurement validity. LLM-based methods establish new state-of-the-art accuracies on multiple causal benchmarks. Algorithms based on GPT-3.5 and 4 outperform existing algorithms on a pairwise causal discovery task (97%, 13 points gain), counterfactual reasoning task (92%, 20 points gain), and actual causality (86% accuracy in determining necessary and sufficient causes in vignettes). At the same time, LLMs exhibit unpredictable failure modes and we provide some techniques to interpret their robustness. Crucially, LLMs perform these causal tasks while relying on sources of knowledge and methods distinct from and complementary to non-LLM based approaches. Specifically, LLMs bring capabilities so far understood to be restricted to humans, such as using collected knowledge to generate causal graphs or identifying background causal context from natural language. We envision LLMs to be used alongside existing causal methods, as a proxy for human domain knowledge and to reduce human effort in setting up a causal analysis, one of the biggest impediments to the widespread adoption of causal methods. We also see existing causal methods as promising tools for LLMs to formalize, validate, and communicate their reasoning especially in high-stakes scenarios. In capturing common sense and domain knowledge about causal mechanisms and supporting translation between natural language and formal methods, LLMs open new frontiers for advancing the research, practice, and adoption of causality.

Selective inference is the problem of giving valid answers to statistical questions chosen in a data-driven manner. A standard solution to selective inference is simultaneous inference, which delivers valid answers to the set of all questions that could possibly have been asked. However, simultaneous inference can be unnecessarily conservative if this set includes many questions that were unlikely to be asked in the first place. We introduce a less conservative solution to selective inference that we call locally simultaneous inference, which only answers those questions that could plausibly have been asked in light of the observed data, all the while preserving rigorous type I error guarantees. For example, if the objective is to construct a confidence interval for the "winning" treatment effect in a clinical trial with multiple treatments, and it is obvious in hindsight that only one treatment had a chance to win, then our approach will return an interval that is nearly the same as the uncorrected, standard interval. Under mild conditions satisfied by common confidence intervals, locally simultaneous inference strictly dominates simultaneous inference, meaning it can never yield less statistical power but only more. Compared to conditional selective inference, which demands stronger guarantees, locally simultaneous inference is more easily applicable in nonparametric settings and is more numerically stable.

In combinatorial causal bandits (CCB), the learning agent chooses a subset of variables in each round to intervene and collects feedback from the observed variables to minimize expected regret or sample complexity. Previous works study this problem in both general causal models and binary generalized linear models (BGLMs). However, all of them require prior knowledge of causal graph structure. This paper studies the CCB problem without the graph structure on binary general causal models and BGLMs. We first provide an exponential lower bound of cumulative regrets for the CCB problem on general causal models. To overcome the exponentially large space of parameters, we then consider the CCB problem on BGLMs. We design a regret minimization algorithm for BGLMs even without the graph skeleton and show that it still achieves $O(\sqrt{T}\ln T)$ expected regret. This asymptotic regret is the same as the state-of-art algorithms relying on the graph structure. Moreover, we sacrifice the regret to $O(T^{\frac{2}{3}}\ln T)$ to remove the weight gap covered by the asymptotic notation. At last, we give some discussions and algorithms for pure exploration of the CCB problem without the graph structure.

Peter Andrews has proposed, in 1971, the problem of finding an analog of the Skolem theorem for Simple Type Theory. A first idea lead to a naive rule that worked only for Simple Type Theory with the axiom of choice and the general case has only been solved, more than ten years later, by Dale Miller. More recently, we have proposed with Th{\'e}r{\`e}se Hardin and Claude Kirchner a new way to prove analogs of the Miller theorem for different, but equivalent, formulations of Simple Type Theory. In this paper, that does not contain new technical results, I try to show that the history of the skolemization problem and of its various solutions is an illustration of a tension between two points of view on Simple Type Theory: the logical and the theoretical points of view.

We study the connections between sorting and the binary search tree (BST) model, with an aim towards showing that the fields are connected more deeply than is currently appreciated. While any BST can be used to sort by inserting the keys one-by-one, this is a very limited relationship and importantly says nothing about parallel sorting. We show what we believe to be the first formal relationship between the BST model and sorting. Namely, we show that a large class of sorting algorithms, which includes mergesort, quicksort, insertion sort, and almost every instance-optimal sorting algorithm, are equivalent in cost to offline BST algorithms. Our main theoretical tool is the geometric interpretation of the BST model introduced by Demaine et al., which finds an equivalence between searches on a BST and point sets in the plane satisfying a certain property. To give an example of the utility of our approach, we introduce the log-interleave bound, a measure of the information-theoretic complexity of a permutation $\pi$, which is within a $\lg \lg n$ multiplicative factor of a known lower bound in the BST model; we also devise a parallel sorting algorithm with polylogarithmic span that sorts a permutation $\pi$ using comparisons proportional to its log-interleave bound. Our aforementioned result on sorting and offline BST algorithms can be used to show existence of an offline BST algorithm whose cost is within a constant factor of the log-interleave bound of any permutation $\pi$.

We study causal inference under case-control and case-population sampling. Specifically, we focus on the binary-outcome and binary-treatment case, where the parameters of interest are causal relative and attributable risks defined via the potential outcome framework. It is shown that strong ignorability is not always as powerful as it is under random sampling and that certain monotonicity assumptions yield comparable results in terms of sharp identified intervals. Specifically, the usual odds ratio is shown to be a sharp identified upper bound on causal relative risk under the monotone treatment response and monotone treatment selection assumptions. We offer algorithms for inference on the causal parameters that are aggregated over the true population distribution of the covariates. We show the usefulness of our approach by studying three empirical examples: the benefit of attending private school for entering a prestigious university in Pakistan; the relationship between staying in school and getting involved with drug-trafficking gangs in Brazil; and the link between physicians' hours and size of the group practice in the United States.

In this paper, we consider the generalization ability of deep wide feedforward ReLU neural networks defined on a bounded domain $\mathcal X \subset \mathbb R^{d}$. We first demonstrate that the generalization ability of the neural network can be fully characterized by that of the corresponding deep neural tangent kernel (NTK) regression. We then investigate on the spectral properties of the deep NTK and show that the deep NTK is positive definite on $\mathcal{X}$ and its eigenvalue decay rate is $(d+1)/d$. Thanks to the well established theories in kernel regression, we then conclude that multilayer wide neural networks trained by gradient descent with proper early stopping achieve the minimax rate, provided that the regression function lies in the reproducing kernel Hilbert space (RKHS) associated with the corresponding NTK. Finally, we illustrate that the overfitted multilayer wide neural networks can not generalize well on $\mathbb S^{d}$.

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.

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.

This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.