Beyond binomial and negative binomial: adaptation in Bernoulli parameter estimation

Estimating the parameter of a Bernoulli process arises in many applications, including photon-efficient active imaging where each illumination period is regarded as a single Bernoulli trial. Motivated by acquisition efficiency when multiple Bernoulli processes (e.g., multiple pixels) are of interest, we formulate the allocation of trials under a constraint on the mean as an optimal resource allocation problem. An oracle-aided trial allocation demonstrates that there can be a significant advantage from varying the allocation for different processes and inspires the introduction of a simple trial allocation gain quantity. Motivated by achieving this gain without an oracle, we present a trellis-based framework for representing and optimizing stopping rules. Considering the convenient case of Beta priors, three implementable stopping rules with similar performances are explored, and the simplest of these is shown to asymptotically achieve the oracle-aided trial allocation. These approaches are further extended to estimating functions of a Bernoulli parameter. In simulations inspired by realistic active imaging scenarios, we demonstrate significant mean-squared error improvements up to 4.36 dB for the estimation of p and up to 1.86 dB for the estimation of log p.https://arxiv.org/abs/1809.08801https://arxiv.org/abs/1809.08801First author draf

Treebank-based acquisition of a Chinese lexical-functional grammar

Scaling wide-coverage, constraint-based grammars such as Lexical-Functional Grammars (LFG) (Kaplan and Bresnan, 1982; Bresnan, 2001) or Head-Driven Phrase Structure Grammars (HPSG) (Pollard and Sag, 1994) from fragments to naturally occurring unrestricted text is knowledge-intensive, time-consuming and (often prohibitively) expensive. A number of researchers have recently presented methods to automatically acquire wide-coverage, probabilistic constraint-based grammatical resources from treebanks (Cahill et al., 2002, Cahill et al., 2003; Cahill et al., 2004; Miyao et al., 2003; Miyao et al., 2004; Hockenmaier and Steedman, 2002; Hockenmaier, 2003), addressing the knowledge acquisition bottleneck in constraint-based grammar development. Research to date has concentrated on English and German. In this paper we report on an experiment to induce wide-coverage, probabilistic LFG grammatical and lexical resources for Chinese from the Penn Chinese Treebank (CTB) (Xue et al., 2002) based on an automatic f-structure annotation algorithm. Currently 96.751% of the CTB trees receive a single, covering and connected f-structure, 0.112% do not receive an f-structure due to feature clashes, while 3.137% are associated with multiple f-structure fragments. From the f-structure-annotated CTB we extract a total of 12975 lexical entries with 20 distinct subcategorisation frame types. Of these 3436 are verbal entries with a total of 11 different frame types. We extract a number of PCFG-based LFG approximations. Currently our best automatically induced grammars achieve an f-score of 81.57% against the trees in unseen articles 301-325; 86.06% f-score (all grammatical functions) and 73.98% (preds-only) against the dependencies derived from the f-structures automatically generated for the original trees in 301-325 and 82.79% (all grammatical functions) and 67.74% (preds-only) against the dependencies derived from the manually annotated gold-standard f-structures for 50 trees randomly selected from articles 301-325

Estimating Middle Tier Acquisition Schedule Risk

Excerpt from the Proceedings of the Nineteenth Annual Acquisition Research SymposiumCongress recently created Middle Tier Acquisition (MTA) programs, which provide the military services rapid prototyping and fielding pathways with new program flexibilities and an explicit schedule constraint. The services are executing multiple MTAs, resulting in a set of MTA experiments related to development, execution, and governance. There is little published information on MTA performance; we use public data to quantify planned schedules. We introduce a quantified schedule risk measure based on Monte Carlo simulations. The simulations provide insights into MTA programs’ schedule risk and program performance relative to a statistically based reference.Approved for public release; distribution is unlimited

Multi-product budget-constrained acquistion and pricing with uncertain demand and supplier quantity discounts

We consider the joint acquisition and pricing problem where the retailer sells multiple products with uncertain demands and the suppliers provide all unit quantity discounts.The problem is to determine the optimal acquisition quantities and selling prices so as to maximize the retailer’s expected profit, subject to a budget constraint. This is the first extension to consider supplier discounts in the constrained multi-product newsvendor pricing problem. We establish a mixed integer nonlinear programming (MINLP) model to formulate the problem, and developaLagrangian based solution approach.Computational results for the test problems involving up to thousand products are reported, which show that the Lagrangian based approach can obtain high-quality solutions in a very short time

Beyond Binomial and Negative Binomial: Adaptation in Bernoulli Parameter Estimation

Estimating the parameter of a Bernoulli process arises in many applications, including photon-efficient active imaging where each illumination period is regarded as a single Bernoulli trial. Motivated by acquisition efficiency when multiple Bernoulli processes are of interest, we formulate the allocation of trials under a constraint on the mean as an optimal resource allocation problem. An oracle-aided trial allocation demonstrates that there can be a significant advantage from varying the allocation for different processes and inspires a simple trial allocation gain quantity. Motivated by realizing this gain without an oracle, we present a trellis-based framework for representing and optimizing stopping rules. Considering the convenient case of Beta priors, three implementable stopping rules with similar performances are explored, and the simplest of these is shown to asymptotically achieve the oracle-aided trial allocation. These approaches are further extended to estimating functions of a Bernoulli parameter. In simulations inspired by realistic active imaging scenarios, we demonstrate significant mean-squared error improvements: up to 4.36 dB for the estimation of p and up to 1.80 dB for the estimation of log p.Comment: 13 pages, 16 figure

Multi-point acquisition function for constraint parallel efficient multi-objective optimization

Bayesian optimization is often used to optimize expensive black box optimization problems with long simulation times. Typically Bayesian optimization algorithms propose one solution per iteration. The downside of this strategy is the sub-optimal use of available computing power. To efficiently use the available computing power (or a number of licenses etc.) we introduce a multi-point acquisition function for parallel efficient multi-objective optimization algorithms. The multi-point acquisition function is based on the hypervolume contribution of multiple solutions simultaneously, leading to well spread solutions along the Pareto frontier. By combining this acquisition function with a constraint handling technique, multiple feasible solutions can be proposed and evaluated in parallel every iteration. The hypervolume and feasibility of the solutions can easily be estimated by using multiple cheap radial basis functions as surrogates with different configurations. The acquisition function can be used with different population sizes and even for one shot optimization. The strength and generalizability of the new acquisition function is demonstrated by optimizing a set of black box constraint multi-objective problem instances. The experiments show a huge time saving factor by using our novel multi-point acquisition function, while only marginally worsening the hypervolume after the same number of function evaluations.Algorithms and the Foundations of Software technolog

Bayesian Optimization with Unknown Constraints

Recent work on Bayesian optimization has shown its effectiveness in global optimization of difficult black-box objective functions. Many real-world optimization problems of interest also have constraints which are unknown a priori. In this paper, we study Bayesian optimization for constrained problems in the general case that noise may be present in the constraint functions, and the objective and constraints may be evaluated independently. We provide motivating practical examples, and present a general framework to solve such problems. We demonstrate the effectiveness of our approach on optimizing the performance of online latent Dirichlet allocation subject to topic sparsity constraints, tuning a neural network given test-time memory constraints, and optimizing Hamiltonian Monte Carlo to achieve maximal effectiveness in a fixed time, subject to passing standard convergence diagnostics.Comment: 14 pages, 3 figure

SART-Type Image Reconstruction from Overlapped Projections

To maximize the time-integrated X-ray flux from multiple X-ray sources and shorten the data acquisition process, a promising way is to allow overlapped projections from multiple sources being simultaneously on without involving the source multiplexing technology. The most challenging task in this configuration is to perform image reconstruction effectively and efficiently from overlapped projections. Inspired by the single-source simultaneous algebraic reconstruction technique (SART), we hereby develop a multisource SART-type reconstruction algorithm regularized by a sparsity-oriented constraint in the soft-threshold filtering framework to reconstruct images from overlapped projections. Our numerical simulation results verify the correctness of the proposed algorithm and demonstrate the advantage of image reconstruction from overlapped projections

English Speaker Acquisition of Topic and Subject in Multiple Clause Sentences in Japanese

This study investigated native English speakers’ acquisition of the constraint for topic-wa and the preference for subject-ga in multiple-clause sentences in Japanese. The constraint for topic-wa is that the topic-wa cannot appear in certain types of subordinate clauses, and the preference for subject-ga is that the overt subject-ga in a subordinate clause should not overlap the topic for a matrix clause. Two sentence-completion experiments were conducted with native English-speaking participants, who were considered advanced-level Japanese learners, as well as native Japanese-speaking participants (the control group). The results indicated that although English speakers followed the constraint for the topic-wa, they frequently used the topic-wa as non-subject topics (unlike native Japanese speakers) when an embedded subordinate clause intervened between the topic-wa and the rest of the matrix clause. Also, English speakers used the same subject-ga for both subordinate and matrix clauses, unlike the native Japanese speakers’ preference. The outcome implies that English speakers associated the topic-wa with English non-subject topics, and the subject-ga with English subjects