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This paper presents a proximal-point-based catalyst scheme for simple first-order methods applied to convex minimization and convex-concave minimax problems. In particular, for smooth and (strongly)-convex minimization problems, the proposed catalyst scheme, instantiated with a simple variant of stochastic gradient method, attains the optimal rate of convergence in terms of both deterministic and stochastic errors. For smooth and strongly-convex-strongly-concave minimax problems, the catalyst scheme attains the optimal rate of convergence for deterministic and stochastic errors up to a logarithmic factor. To the best of our knowledge, this reported convergence seems to be attained for the first time by stochastic first-order methods in the literature. We obtain this result by designing and catalyzing a novel variant of stochastic extragradient method for solving smooth and strongly-monotone variational inequality, which may be of independent interest.

Accurate cancer risk estimation is crucial to clinical decision-making, such as identifying high-risk people for screening. However, most existing cancer risk models incorporate data from epidemiologic studies, which usually cannot represent the target population. While population-based health surveys are ideal for making inference to the target population, they typically do not collect time-to-cancer incidence data. Instead, time-to-cancer specific mortality is often readily available on surveys via linkage to vital statistics. We develop calibrated pseudoweighting methods that integrate individual-level data from a cohort and a survey, and summary statistics of cancer incidence from national cancer registries. By leveraging individual-level cancer mortality data in the survey, the proposed methods impute time-to-cancer incidence for survey sample individuals and use survey calibration with auxiliary variables of influence functions generated from Cox regression to improve robustness and efficiency of the inverse-propensity pseudoweighting method in estimating pure risks. We develop a lung cancer incidence pure risk model from the Prostate, Lung, Colorectal, and Ovarian (PLCO) Cancer Screening Trial using our proposed methods by integrating data from the National Health Interview Survey (NHIS) and cancer registries.

Accurate position and posture measurements of the freely-falling test mass are crucial for the success of spaceborne gravitational wave detection missions. This paper presents a novel laboratory-developed test mass motion readout that utilizes quadrant photodetectors to measure the translation and tilt of a test mass. Departing from conventional methods like Zeeman effect or AOM frequency shift modulation, the readout system employs the phase locking of two lasers to generate the dual-frequency heterodyne source. Notably, the out-of-loop sensitivity of the phase locking reaches below 30 pm/Hz1/2 within the frequency band of 1 mHz and 10 Hz. The system comprises three measurement interferometers and one reference interferometer, featuring a symmetric design that enables measurements of up to six degrees of freedom based on polarization-multiplexing and differential wavefront sensing. Ground-simulated experimental results demonstrate that the proposed system has achieved a measurement sensitivity of 4 pm/Hz1/2 and 2 nrad/Hz1/2 at 1 Hz, a resolution of 5 nm and 0.1 urad, a range of 200 um and 600 urad, respectively. These findings showcase the system's potential as an alternative method for precisely monitoring the motion of test masses in spaceborne gravitational wave detection missions and other applications requiring accurate positioning and multi-degrees-of-freedom sensing., Comment: 7 pages, 10 figures. arXiv admin note: substantial text overlap with arXiv:2207.06420

In the paper, by virtue of the famous formula of Fa\`a di Bruno, with the aid of several identities of partial Bell polynomials, by means of a formula for derivatives of the ratio of two differentiable functions, and with availability of other techniques, the authors establish closed-form formulas in terms of the Bernoulli numbers and the second kind Stirling numbers, present determinantal expressions, derive recursive relations, obtain power series, and compute special values of the function $\frac{v^j}{1-\operatorname{e}^{-v}}$, its derivatives, and related ones used in Clark--Ismail's two conjectures. By these results, the authors also discover a formula for the determinant of a Hessenberg matrix and derive logarithmic convexity of a sequence related to the function and its derivatives., Comment: 23 pages

Multi-Agent Reinforcement Learning (MARL) has shown promising results across several domains. Despite this promise, MARL policies often lack robustness and are therefore sensitive to small changes in their environment. This presents a serious concern for the real world deployment of MARL algorithms, where the testing environment may slightly differ from the training environment. In this work we show that we can gain robustness by controlling a policy's Lipschitz constant, and under mild conditions, establish the existence of a Lipschitz and close-to-optimal policy. Based on these insights, we propose a new robust MARL framework, ERNIE, that promotes the Lipschitz continuity of the policies with respect to the state observations and actions by adversarial regularization. The ERNIE framework provides robustness against noisy observations, changing transition dynamics, and malicious actions of agents. However, ERNIE's adversarial regularization may introduce some training instability. To reduce this instability, we reformulate adversarial regularization as a Stackelberg game. We demonstrate the effectiveness of the proposed framework with extensive experiments in traffic light control and particle environments. In addition, we extend ERNIE to mean-field MARL with a formulation based on distributionally robust optimization that outperforms its non-robust counterpart and is of independent interest. Our code is available at https://github.com/abukharin3/ERNIE., Comment: 33 pages, 10 figures

Identifying replicable signals across different studies provides stronger scientific evidence and more powerful inference. Existing literature on high dimensional applicability analysis either imposes strong modeling assumptions or has low power. We develop a powerful and robust empirical Bayes approach for high dimensional replicability analysis. Our method effectively borrows information from different features and studies while accounting for heterogeneity. We show that the proposed method has better power than competing methods while controlling the false discovery rate, both empirically and theoretically. Analyzing datasets from the genome-wide association studies reveals new biological insights that otherwise cannot be obtained by using existing methods.

Recent advancements in large language models (LLMs) have demonstrated remarkable abilities in handling a variety of natural language processing (NLP) downstream tasks, even on mathematical tasks requiring multi-step reasoning. In this report, we introduce the KwaiYiiMath which enhances the mathematical reasoning abilities of KwaiYiiBase1, by applying Supervised Fine-Tuning (SFT) and Reinforced Learning from Human Feedback (RLHF), including on both English and Chinese mathematical tasks. Meanwhile, we also constructed a small-scale Chinese primary school mathematics test set (named KMath), consisting of 188 examples to evaluate the correctness of the problem-solving process generated by the models. Empirical studies demonstrate that KwaiYiiMath can achieve state-of-the-art (SOTA) performance on GSM8k, CMath, and KMath compared with the similar size models, respectively., Comment: technical report. arXiv admin note: text overlap with arXiv:2306.16636 by other authors

Recently, order-preserving pattern (OPP) mining, a new sequential pattern mining method, has been proposed to mine frequent relative orders in a time series. Although frequent relative orders can be used as features to classify a time series, the mined patterns do not reflect the differences between two classes of time series well. To effectively discover the differences between time series, this paper addresses the top-k contrast OPP (COPP) mining and proposes a COPP-Miner algorithm to discover the top-k contrast patterns as features for time series classification, avoiding the problem of improper parameter setting. COPP-Miner is composed of three parts: extreme point extraction to reduce the length of the original time series, forward mining, and reverse mining to discover COPPs. Forward mining contains three steps: group pattern fusion strategy to generate candidate patterns, the support rate calculation method to efficiently calculate the support of a pattern, and two pruning strategies to further prune candidate patterns. Reverse mining uses one pruning strategy to prune candidate patterns and consists of applying the same process as forward mining. Experimental results validate the efficiency of the proposed algorithm and show that top-k COPPs can be used as features to obtain a better classification performance.

We fit the UV/optical lightcurves of the Seyfert 1 galaxy Mrk 817 to produce maps of the accretion disk temperature fluctuations $\delta T$ resolved in time and radius. The $\delta T$ maps are dominated by coherent radial structures that move slowly ($v \ll c$) inwards and outwards, which conflicts with the idea that disk variability is driven only by reverberation. Instead, these slow-moving temperature fluctuations are likely due to variability intrinsic to the disk. We test how modifying the input lightcurves by smoothing and subtracting them changes the resulting $\delta T$ maps and find that most of the temperature fluctuations exist over relatively long timescales ($\sim$100s of days). We show how detrending AGN lightcurves can be used to separate the flux variations driven by the slow-moving temperature fluctuations from those driven by reverberation. We also simulate contamination of the continuum emission from the disk by continuum emission from the broad line region (BLR), which is expected to have spectral features localized in wavelength, such as the Balmer break contaminating the $U$ band. We find that a disk with a smooth temperature profile cannot produce a signal localized in wavelength and that any BLR contamination should appear as residuals in our model lightcurves. Given the observed residuals, we estimate that only $\sim$20% of the variable flux in the $U$ and $u$ lightcurves can be due to BLR contamination. Finally, we discus how these maps not only describe the data, but can make predictions about other aspects of AGN variability., Comment: 23 pages, 18 figures, submitting to ApJ, comments welcome