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1. Rate-Optimal Budget Allocation for the Probability of Good Selection

   https://doi.org/10.1109/WSC63780.2024.10838732  

   Kim, Taeho; Eckman, David J (December 2024, IEEE)

   Lam, H; Azar, E; Batur, D; Gao, S; Xie, W; Hunter, S R; Rossetti, M D (Ed.)

   This paper studies the allocation of simulation effort in a ranking-and-selection (R&S) problem with the goal of selecting a system whose performance is within a given tolerance of the best. We apply large-deviations theory to derive an optimal allocation for maximizing the rate at which the so-called probability of good selection (PGS) asymptotically approaches one, assuming that systems’ output distributions are known. An interesting property of the optimal allocation is that some good systems may receive a sampling ratio of zero. We demonstrate through numerical experiments that this property leads to serious practical consequences, specifically when designing adaptive R&S algorithms. In particular, we observe that the convergence and even consistency of a simple plug-in algorithm designed for the PGS goal can be negatively impacted. We offer empirical evidence of these challenges and a preliminary exploration of a potential correction. 

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2. A spatiotemporal recommendation engine for malaria control

   https://doi.org/10.1093/biostatistics/kxab010  

   Guan, Qian; Reich, Brian J; Laber, Eric B (April 2021, Biostatistics)

   Summary Malaria is an infectious disease affecting a large population across the world, and interventions need to be efficiently applied to reduce the burden of malaria. We develop a framework to help policy-makers decide how to allocate limited resources in realtime for malaria control. We formalize a policy for the resource allocation as a sequence of decisions, one per intervention decision, that map up-to-date disease related information to a resource allocation. An optimal policy must control the spread of the disease while being interpretable and viewed as equitable to stakeholders. We construct an interpretable class of resource allocation policies that can accommodate allocation of resources residing in a continuous domain and combine a hierarchical Bayesian spatiotemporal model for disease transmission with a policy-search algorithm to estimate an optimal policy for resource allocation within the pre-specified class. The estimated optimal policy under the proposed framework improves the cumulative long-term outcome compared with naive approaches in both simulation experiments and application to malaria interventions in the Democratic Republic of the Congo. 

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3. Learning from Binary Multiway Data: Probabilistic Tensor Decomposition and Its Statistical Optimality

   Wang, Miaoyan; Li, Lexin (July 2020, Journal of machine learning research)

   We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a multilinear Bernoulli model, develop a rank-constrained likelihood-based estimation method, and obtain the theoretical accuracy guarantees. In contrast to continuous-valued problems, the binary tensor problem exhibits an interesting phase transition phenomenon according to the signal-to-noise ratio. The error bound for the parameter tensor estimation is established, and we show that the obtained rate is minimax optimal under the considered model. Furthermore, we develop an alternating optimization algorithm with convergence guarantees. The efficacy of our approach is demonstrated through both simulations and analyses of multiple data sets on the tasks of tensor completion and clustering. 

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4. Computing on Functions Using Randomized Vector Representations

   Frady, E. Paxon; Kleyko, Denis; Kymn, Christopher J.; Olshausen, Bruno A.; Sommer, Friedrich T. (September 2021, ArXivorg)

   null (Ed.)

   Vector space models for symbolic processing that encode symbols by random vectors have been proposed in cognitive science and connectionist communities under the names Vector Symbolic Architecture (VSA), and, synonymously, Hyperdimensional (HD) computing. In this paper, we generalize VSAs to function spaces by mapping continuous-valued data into a vector space such that the inner product between the representations of any two data points represents a similarity kernel. By analogy to VSA, we call this new function encoding and computing framework Vector Function Architecture (VFA). In VFAs, vectors can represent individual data points as well as elements of a function space (a reproducing kernel Hilbert space). The algebraic vector operations, inherited from VSA, correspond to well-defined operations in function space. Furthermore, we study a previously proposed method for encoding continuous data, fractional power encoding (FPE), which uses exponentiation of a random base vector to produce randomized representations of data points and fulfills the kernel properties for inducing a VFA. We show that the distribution from which elements of the base vector are sampled determines the shape of the FPE kernel, which in turn induces a VFA for computing with band-limited functions. In particular, VFAs provide an algebraic framework for implementing large-scale kernel machines with random features, extending Rahimi and Recht, 2007. Finally, we demonstrate several applications of VFA models to problems in image recognition, density estimation and nonlinear regression. Our analyses and results suggest that VFAs constitute a powerful new framework for representing and manipulating functions in distributed neural systems, with myriad applications in artificial intelligence. 

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5. Universal Hypothesis Testing with Kernels: Asymptotically Optimal Tests for Goodness of Fit

   Zhu, Shengyu; Chen, Biao; Yang, Pengfei; Chen, Zhitang (April 2019, International Conference on Artificial Intelligence and Statistics)

   We characterize the asymptotic performance of nonparametric goodness of fit testing. The exponential decay rate of the type-II error probability is used as the asymptotic performance metric, and a test is optimal if it achieves the maximum rate subject to a constant level constraint on the type-I error probability. We show that two classes of Maximum Mean Discrepancy (MMD) based tests attain this optimality on Rd, while the quadratictime Kernel Stein Discrepancy (KSD) based tests achieve the maximum exponential decay rate under a relaxed level constraint. Under the same performance metric, we proceed to show that the quadratic-time MMD based two-sample tests are also optimal for general two-sample problems, provided that kernels are bounded continuous and characteristic. Key to our approach are Sanov’s theorem from large deviation theory and the weak metrizable properties of the MMD and KSD. 

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