统计能力是对假设检验的优点/强度的度量。正式地，如果存在真实的效果，则是检测效果的概率。因此，需要优化统计能力作为假设检验的某些参数的函数。但是，对于大多数假设检验，统计功率的显式功能形式是这些参数的函数是未知的，但是使用模拟实验可以计算给定值集值的统计功率。这些模拟实验通常在计算上很昂贵。因此，使用模拟开发整个统计功率歧管可能非常耗时。由此激励，我们提出了一种基于遗传算法的新型统计功率歧管框架。对于多个线性回归$ f $检验，我们表明所提出的算法/框架与蛮力方法相比，随着电源甲骨文的查询数量大大减少，统计功率歧管的速度要快得多。我们还表明，随着遗传算法的增加，学习流形的质量会提高。

越来越承认，具有多种模型参数的计划研究的先验统计功率估计本质上是多变量问题。对于个人感兴趣的各个参数的电源无法可靠地估计，因为相对于一个参数的可变地，与一个参数进行相关性和方差，将影响另一个参数的权力，所有通常的单变量的考虑因素都是平等的。在这种情况下，特别是对于具有许多参数的模型的明确解决方案是不切实际或无法解决的，将研究人员与模拟功率的普遍方法进行。然而，模型参数矢量的点估计是不确定的，并且不准确的影响是未知的。在这种情况下，建议使用灵敏度分析，使得模拟可能的可观察参数向量的多种组合以了解电力折衷。对这种方法的限制是，它可以计算得昂贵的昂贵的组合，以便在社会科学家估计的模型中精确地映射越来越高的尺寸空间中的电力折衷功能。本文探讨了对不同模型参数组合的研究的有效估计和绘图。最佳地通电研究对于确保找到假设效果的最小可能性是至关重要的。我们首先展示改变参数值对特定假设的功率的影响，并在给定的精度水平上量化计算这种图的计算强度。最后，我们提出了一种简单宽大的机器学习灵感的解决方案，将计算成本降低到少于7 \％的可能被称为蛮力方法。 [简略]

While the capabilities of autonomous systems have been steadily improving in recent years, these systems still struggle to rapidly explore previously unknown environments without the aid of GPS-assisted navigation. The DARPA Subterranean (SubT) Challenge aimed to fast track the development of autonomous exploration systems by evaluating their performance in real-world underground search-and-rescue scenarios. Subterranean environments present a plethora of challenges for robotic systems, such as limited communications, complex topology, visually-degraded sensing, and harsh terrain. The presented solution enables long-term autonomy with minimal human supervision by combining a powerful and independent single-agent autonomy stack, with higher level mission management operating over a flexible mesh network. The autonomy suite deployed on quadruped and wheeled robots was fully independent, freeing the human supervision to loosely supervise the mission and make high-impact strategic decisions. We also discuss lessons learned from fielding our system at the SubT Final Event, relating to vehicle versatility, system adaptability, and re-configurable communications.

We consider the problem of constructing minimax rate-optimal estimators for a doubly robust nonparametric functional that has witnessed applications across the causal inference and conditional independence testing literature. Minimax rate-optimal estimators for such functionals are typically constructed through higher-order bias corrections of plug-in and one-step type estimators and, in turn, depend on estimators of nuisance functions. In this paper, we consider a parallel question of interest regarding the optimality and/or sub-optimality of plug-in and one-step bias-corrected estimators for the specific doubly robust functional of interest. Specifically, we verify that by using undersmoothing and sample splitting techniques when constructing nuisance function estimators, one can achieve minimax rates of convergence in all H\"older smoothness classes of the nuisance functions (i.e. the propensity score and outcome regression) provided that the marginal density of the covariates is sufficiently regular. Additionally, by demonstrating suitable lower bounds on these classes of estimators, we demonstrate the necessity to undersmooth the nuisance function estimators to obtain minimax optimal rates of convergence.

Generative AI has matured to a point where large-scale models can generate text that seems indistinguishable from human-written text and remarkably photorealistic images. Automatically measuring how close the distribution of generated data is to the target real data distribution is a key step in diagnosing existing models and developing better models. We present MAUVE, a family of comparison measures between pairs of distributions such as those encountered in the generative modeling of text or images. These scores are statistical summaries of divergence frontiers capturing two types of errors in generative modeling. We explore four approaches to statistically estimate these scores: vector quantization, non-parametric estimation, classifier-based estimation, and parametric Gaussian approximations. We provide statistical bounds for the vector quantization approach. Empirically, we find that the proposed scores paired with a range of $f$-divergences and statistical estimation methods can quantify the gaps between the distributions of human-written text and those of modern neural language models by correlating with human judgments and identifying known properties of the generated texts. We conclude the paper by demonstrating its applications to other AI domains and discussing practical recommendations.

Tensor robust principal component analysis (RPCA), which seeks to separate a low-rank tensor from its sparse corruptions, has been crucial in data science and machine learning where tensor structures are becoming more prevalent. While powerful, existing tensor RPCA algorithms can be difficult to use in practice, as their performance can be sensitive to the choice of additional hyperparameters, which are not straightforward to tune. In this paper, we describe a fast and simple self-supervised model for tensor RPCA using deep unfolding by only learning four hyperparameters. Despite its simplicity, our model expunges the need for ground truth labels while maintaining competitive or even greater performance compared to supervised deep unfolding. Furthermore, our model is capable of operating in extreme data-starved scenarios. We demonstrate these claims on a mix of synthetic data and real-world tasks, comparing performance against previously studied supervised deep unfolding methods and Bayesian optimization baselines.

Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving math problems and proving theorems has garnered significant interest in the fields of machine learning and natural language processing. For example, mathematics serves as a testbed for aspects of reasoning that are challenging for powerful deep learning models, driving new algorithmic and modeling advances. On the other hand, recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning. In this survey paper, we review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. We also evaluate existing benchmarks and methods, and discuss future research directions in this domain.

When designing a new API for a large project, developers need to make smart design choices so that their code base can grow sustainably. To ensure that new API components are well designed, developers can learn from existing API components. However, the lack of standardized method for comparing API designs makes this learning process time-consuming and difficult. To address this gap we developed the API-Spector, to the best of our knowledge one of the first API-to-API specification recommendation engines. API-Spector retrieves relevant specification components written in OpenAPI (a widely adopted language used to describe web APIs). API-Spector presents several significant contributions, including: (1) novel methods of processing and extracting key information from OpenAPI specifications, (2) innovative feature extraction techniques that are optimized for the highly technical API specification domain, and (3) a novel log-linear probabilistic model that combines multiple signals to retrieve relevant and high quality OpenAPI specification components given a query specification. We evaluate API-Spector in both quantitative and qualitative tasks and achieve an overall of 91.7% recall@1 and 56.2% F1, which surpasses baseline performance by 15.4% in recall@1 and 3.2% in F1. Overall, API-Spector will allow developers to retrieve relevant OpenAPI specification components from a public or internal database in the early stages of the API development cycle, so that they can learn from existing established examples and potentially identify redundancies in their work. It provides the guidance developers need to accelerate development process and contribute thoughtfully designed APIs that promote code maintainability and quality.

Vehicle routing problems and other combinatorial optimization problems have been approximately solved by reinforcement learning agents with policies based on encoder-decoder models with attention mechanisms. These techniques are of substantial interest but still cannot solve the complex routing problems that arise in a realistic setting which can have many trucks and complex requirements. With the aim of making reinforcement learning a viable technique for supply chain optimization, we develop new extensions to encoder-decoder models for vehicle routing that allow for complex supply chains using classical computing today and quantum computing in the future. We make two major generalizations. First, our model allows for routing problems with multiple trucks. Second, we move away from the simple requirement of having a truck deliver items from nodes to one special depot node, and instead allow for a complex tensor demand structure. We show how our model, even if trained only for a small number of trucks, can be embedded into a large supply chain to yield viable solutions.

Problem instances of a size suitable for practical applications are not likely to be addressed during the noisy intermediate-scale quantum (NISQ) period with (almost) pure quantum algorithms. Hybrid classical-quantum algorithms have potential, however, to achieve good performance on much larger problem instances. We investigate one such hybrid algorithm on a problem of substantial importance: vehicle routing for supply chain logistics with multiple trucks and complex demand structure. We use reinforcement learning with neural networks with embedded quantum circuits. In such neural networks, projecting high-dimensional feature vectors down to smaller vectors is necessary to accommodate restrictions on the number of qubits of NISQ hardware. However, we use a multi-head attention mechanism where, even in classical machine learning, such projections are natural and desirable. We consider data from the truck routing logistics of a company in the automotive sector, and apply our methodology by decomposing into small teams of trucks, and we find results comparable to human truck assignment.