We study hypothesis testing over a heterogeneous population of strategic agents with private information. Any single test applied uniformly across the population yields statistical error that is sub-optimal relative to the performance of an oracle given access to the private information. We show how it is possible to design menus of statistical contracts that pair type-optimal tests with payoff structures, inducing agents to self-select according to their private information. This separating menu elicits agent types and enables the principal to match the oracle performance even without a priori knowledge of the agent type. Our main result fully characterizes the collection of all separating menus that are instance-adaptive, matching oracle performance for an arbitrary population of heterogeneous agents. We identify designs where information elicitation is essentially costless, requiring negligible additional expense relative to a single-test benchmark, while improving statistical performance. Our work establishes a connection between proper scoring rules and menu design, showing how the structure of the hypothesis test constrains the elicitable information. Numerical examples illustrate the geometry of separating menus and the improvements they deliver in error trade-offs. Overall, our results connect statistical decision theory with mechanism design, demonstrating how heterogeneity and strategic participation can be harnessed to improve efficiency in hypothesis testing.

Bayesian optimization (BO) is effective for expensive black-box problems but remains challenging in high dimensions. We propose NeST-BO, a local BO method that targets the Newton step by jointly learning gradient and Hessian information with Gaussian process surrogates, and selecting evaluations via a one-step lookahead bound on Newton-step error. We show that this bound (and hence the step error) contracts with batch size, so NeST-BO directly inherits inexact-Newton convergence: global progress under mild stability assumptions and quadratic local rates once steps are sufficiently accurate. To scale, we optimize the acquisition in low-dimensional subspaces (e.g., random embeddings or learned sparse subspaces), reducing the dominant cost of learning curvature from $O(d^2)$ to $O(m^2)$ with $m \ll d$ while preserving step targeting. Across high-dimensional synthetic and real-world problems, including cases with thousands of variables and unknown active subspaces, NeST-BO consistently yields faster convergence and lower regret than state-of-the-art local and high-dimensional BO baselines.

The primary purpose of this paper is to present the concept of dichotomy in image illumination modeling based on the power function. In particular, we review several mathematical properties of the power function to identify the limitations and propose a new mathematical model capable of abstracting illumination dichotomy. The simplicity of the equation opens new avenues for classical and modern image analysis and processing. The article provides practical and illustrative image examples to explain how the new model manages dichotomy in image perception. The article shows dichotomy image space as a viable way to extract rich information from images despite poor contrast linked to tone, lightness, and color perception. Moreover, a comparison with state-of-the-art methods in image enhancement provides evidence of the method's value.

Deep Q-network algorithm is used to select economic span of bridge. Selection of bridge span has a significant impact on the total cost of bridge, and a reasonable selection of span can reduce engineering cost. Economic span of bridge is theoretically analyzed, and the theoretical solution formula of economic span is deduced. Construction process of bridge simulation environment is described in detail, including observation space, action space and reward function of the environment. Agent is constructed, convolutional neural network is used to approximate Q function,{\epsilon} greedy policy is used for action selection, and experience replay is used for training. The test verifies that the agent can successfully learn optimal policy and realize economic span selection of bridge. This study provides a potential decision-making tool for bridge design.

This paper studies the approximation of smooth functionals defined over a reproducing kernel Hilbert space (RKHS) using tanh neural networks. A functional maps from a space of functions that has infinite dimensions to R. In recent years, neural networks have been widely employed in operator learning tasks. We are interested in investigating their capability to approximate nonlinear functionals, a special type of operator. Neural networks have been known as universal approximators since [Cybenko, 1989], i.e., to approximate any continuous function, mapping a finite-dimensional input space into another finite-dimensional output space, to arbitrary accuracy. These days, many interesting tasks entail learning operators, i.e., mappings between an infinite-dimensional input Banach space and (possibly) an infinite-dimensional output space. A prototypical example in scientific computing is to map the initial datum into the (time series of) solution of a nonlinear time-dependent partial differential equation (PDE). A priori, it is unclear if neural networks can be successfully employed to learn such operators from data, given that their universality only pertains to finite-dimensional functions. One of the first successful uses of neural networks in the context of operator learning was provided by [Chen and Chen, 1995].

Recent years have seen tremendous advances in the theory and application of sequential experiments. While these experiments are not always designed with hypothesis testing in mind, researchers may still be interested in performing tests after the experiment is completed. The purpose of this paper is to aid in the development of optimal tests for sequential experiments by analyzing their asymptotic properties. Our key finding is that the asymptotic power function of any test can be matched by a test in a limit experiment where a Gaussian process is observed for each treatment, and inference is made for the drifts of these processes. This result has important implications, including a powerful sufficiency result: any candidate test only needs to rely on a fixed set of statistics, regardless of the type of sequential experiment. These statistics are the number of times each treatment has been sampled by the end of the experiment, along with final value of the score (for parametric models) or efficient influence function (for non-parametric models) process for each treatment. We then characterize asymptotically optimal tests under various restrictions such as unbiasedness, \alpha-spending constraints etc. Finally, we apply our our results to three key classes of sequential experiments: costly sampling, group sequential trials, and bandit experiments, and show how optimal inference can be conducted in these scenarios.

In this study, we focus on nonlinear compression methods in spectral features for speaker verification based on deep neural network. We consider different kinds of channel-dependent (CD) nonlinear compression methods optimized in a data-driven manner. Our methods are based on power nonlinearities and dynamic range compression (DRC). We also propose multi-regime (MR) design on the nonlinearities, at improving robustness. Results on VoxCeleb1 and VoxMovies data demonstrate improvements brought by proposed compression methods over both the commonly-used logarithm and their static counterparts, especially for ones based on power function. While CD generalization improves performance on VoxCeleb1, MR provides more robustness on VoxMovies, with a maximum relative equal error rate reduction of 21.6%.

In recent years a lot more CRO & A/B testing practitioners have started paying more attention to the statistical power of their online experiments, at least based on my observations. While this a positive development for which I hope I had contributed somewhat, it comes with the inevitable confusions and misunderstandings surrounding a complex concept such as statistical power. Some of them appear to be so common that they can be termed'myths'. Here we'll dispel three of the most common myths and I will also offer a brief advice on how to avoid all confusions related to the power of an A/B test. However, I will not discuss what statistical power is and how to compute it.