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This paper establishes a combinatorial central limit theorem for stratified randomization that holds under Lindeberg-type conditions and allows for a growing number of large and small strata. The result is then applied to derive the asymptotic distributions of two test statistics proposed in a finite population setting with randomly assigned instruments and a super population instrumental variables model, both having many strata.

We provide efficient replicable algorithms for the problem of learning large-margin halfspaces. Our results improve upon the algorithms provided by Impagliazzo, Lei, Pitassi, and Sorrell [STOC, 2022]. We design the first dimension-independent replicable algorithms for this task which runs in polynomial time, is proper, and has strictly improved sample complexity compared to the one achieved by Impagliazzo et al. [2022] with respect to all the relevant parameters. Moreover, our first algorithm has sample complexity that is optimal with respect to the accuracy parameter $\epsilon$. We also design an SGD-based replicable algorithm that, in some parameters' regimes, achieves better sample and time complexity than our first algorithm. Departing from the requirement of polynomial time algorithms, using the DP-to-Replicability reduction of Bun, Gaboardi, Hopkins, Impagliazzo, Lei, Pitassi, Sorrell, and Sivakumar [STOC, 2023], we show how to obtain a replicable algorithm for large-margin halfspaces with improved sample complexity with respect to the margin parameter $\tau$, but running time doubly exponential in $1/\tau^2$ and worse sample complexity dependence on $\epsilon$ than one of our previous algorithms. We then design an improved algorithm with better sample complexity than all three of our previous algorithms and running time exponential in $1/\tau^{2}$.

We describe a data-efficient, kernel-based approach to statistical testing of conditional independence. A major challenge of conditional independence testing, absent in tests of unconditional independence, is to obtain the correct test level (the specified upper bound on the rate of false positives), while still attaining competitive test power. Excess false positives arise due to bias in the test statistic, which is obtained using nonparametric kernel ridge regression. We propose three methods for bias control to correct the test level, based on data splitting, auxiliary data, and (where possible) simpler function classes. We show these combined strategies are effective both for synthetic and real-world data.

Large Language Models (LLMs) have demonstrated remarkable problem-solving and basic mathematics abilities. However, their efficacy is highly contingent on the formulation of the prompt. This study endeavors to quantify the influence of incorporating "positive thinking" into the system message of the prompt, then compare that to systematic prompt optimization. We assess the performance of 60 combinations of system message snippets, tested with and without Chain of Thought prompting, across three models with parameters ranging from 7 to 70 billion on the GSM8K dataset. Our findings reveal that results do not universally generalize across models. In most instances, the inclusion of "positive thinking" prompts positively affected model performance. Notably, however, Llama2-70B exhibited an exception when not utilizing Chain of Thought, as the optimal system message was found to be none at all. Given the combinatorial complexity, and thus computation time, of experimenting with hand-tuning prompts for large black-box models, we then compared the performance of the best "positive thinking" prompt against the output of systematic prompt optimization. We show that employing an automated prompt optimizer emerges as the most effective method for enhancing performance, even when working with smaller open-source models. Additionally, our findings reveal that the highest-scoring, automatically-optimized prompt exhibits a degree of peculiarity far beyond expectations.

This paper studies the case of possibly high-dimensional covariates in the regression discontinuity design (RDD) analysis. In particular, we propose estimation and inference methods for the RDD models with covariate selection which perform stably regardless of the number of covariates. The proposed methods combine the local approach using kernel weights with $\ell_{1}$-penalization to handle high-dimensional covariates. We provide theoretical and numerical results which illustrate the usefulness of the proposed methods. Theoretically, we present risk and coverage properties for our point estimation and inference methods, respectively. Under certain special case, the proposed estimator becomes more efficient than the conventional covariate adjusted estimator at the cost of an additional sparsity condition. Numerically, our simulation experiments and empirical example show the robust behaviors of the proposed methods to the number of covariates in terms of bias and variance for point estimation and coverage probability and interval length for inference.

This paper proposes SplitSGD, a new dynamic learning rate schedule for stochastic optimization. This method decreases the learning rate for better adaptation to the local geometry of the objective function whenever a stationary phase is detected, that is, the iterates are likely to bounce at around a vicinity of a local minimum. The detection is performed by splitting the single thread into two and using the inner product of the gradients from the two threads as a measure of stationarity. Owing to this simple yet provably valid stationarity detection, SplitSGD is easy-to-implement and essentially does not incur additional computational cost than standard SGD. Through a series of extensive experiments, we show that this method is appropriate for both convex problems and training (non-convex) neural networks, with performance compared favorably to other stochastic optimization methods. Importantly, this method is observed to be very robust with a set of default parameters for a wide range of problems and, moreover, can yield better generalization performance than other adaptive gradient methods such as Adam.

This paper surveys research works in the quickly advancing field of instruction tuning (IT), a crucial technique to enhance the capabilities and controllability of large language models (LLMs). Instruction tuning refers to the process of further training LLMs on a dataset consisting of \textsc{(instruction, output)} pairs in a supervised fashion, which bridges the gap between the next-word prediction objective of LLMs and the users' objective of having LLMs adhere to human instructions. In this work, we make a systematic review of the literature, including the general methodology of IT, the construction of IT datasets, the training of IT models, and applications to different modalities, domains and applications, along with an analysis on aspects that influence the outcome of IT (e.g., generation of instruction outputs, size of the instruction dataset, etc). We also review the potential pitfalls of IT along with criticism against it, along with efforts pointing out current deficiencies of existing strategies and suggest some avenues for fruitful research.

This paper offers a comprehensive review of the research on Natural Language Generation (NLG) over the past two decades, especially in relation to data-to-text generation and text-to-text generation deep learning methods, as well as new applications of NLG technology. This survey aims to (a) give the latest synthesis of deep learning research on the NLG core tasks, as well as the architectures adopted in the field; (b) detail meticulously and comprehensively various NLG tasks and datasets, and draw attention to the challenges in NLG evaluation, focusing on different evaluation methods and their relationships; (c) highlight some future emphasis and relatively recent research issues that arise due to the increasing synergy between NLG and other artificial intelligence areas, such as computer vision, text and computational creativity.

This paper serves as a survey of recent advances in large margin training and its theoretical foundations, mostly for (nonlinear) deep neural networks (DNNs) that are probably the most prominent machine learning models for large-scale data in the community over the past decade. We generalize the formulation of classification margins from classical research to latest DNNs, summarize theoretical connections between the margin, network generalization, and robustness, and introduce recent efforts in enlarging the margins for DNNs comprehensively. Since the viewpoint of different methods is discrepant, we categorize them into groups for ease of comparison and discussion in the paper. Hopefully, our discussions and overview inspire new research work in the community that aim to improve the performance of DNNs, and we also point to directions where the large margin principle can be verified to provide theoretical evidence why certain regularizations for DNNs function well in practice. We managed to shorten the paper such that the crucial spirit of large margin learning and related methods are better emphasized.

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.