Level-Based Analysis of the Population-Based Incremental Learning Algorithm

The Population-Based Incremental Learning (PBIL) algorithm uses a convex combination of the current model and the empirical model to construct the next model, which is then sampled to generate offspring. The Univariate Marginal Distribution Algorithm (UMDA) is a special case of the PBIL, where the current model is ignored. Dang and Lehre (GECCO 2015) showed that UMDA can optimise LeadingOnes efficiently. The question still remained open if the PBIL performs equally well. Here, by applying the level-based theorem in addition to Dvoretzky--Kiefer--Wolfowitz inequality, we show that the PBIL optimises function LeadingOnes in expected time $\mathcal{O}(n\lambda \log \lambda + n^2)$ for a population size $\lambda = \Omega(\log n)$, which matches the bound of the UMDA. Finally, we show that the result carries over to BinVal, giving the fist runtime result for the PBIL on the BinVal problem.Comment: To appea

A frequentist framework of inductive reasoning

Reacting against the limitation of statistics to decision procedures, R. A. Fisher proposed for inductive reasoning the use of the fiducial distribution, a parameter-space distribution of epistemological probability transferred directly from limiting relative frequencies rather than computed according to the Bayes update rule. The proposal is developed as follows using the confidence measure of a scalar parameter of interest. (With the restriction to one-dimensional parameter space, a confidence measure is essentially a fiducial probability distribution free of complications involving ancillary statistics.) A betting game establishes a sense in which confidence measures are the only reliable inferential probability distributions. The equality between the probabilities encoded in a confidence measure and the coverage rates of the corresponding confidence intervals ensures that the measure's rule for assigning confidence levels to hypotheses is uniquely minimax in the game. Although a confidence measure can be computed without any prior distribution, previous knowledge can be incorporated into confidence-based reasoning. To adjust a p-value or confidence interval for prior information, the confidence measure from the observed data can be combined with one or more independent confidence measures representing previous agent opinion. (The former confidence measure may correspond to a posterior distribution with frequentist matching of coverage probabilities.) The representation of subjective knowledge in terms of confidence measures rather than prior probability distributions preserves approximate frequentist validity.Comment: major revisio

Effectiveness of physiotherapy exercise following hip arthroplasty for osteoarthritis: a systematic review of clinical trials

Background: Physiotherapy has long been a routine component of patient rehabilitation following hip joint replacement. The purpose of this systematic review was to evaluate the effectiveness of physiotherapy exercise after discharge from hospital on function, walking, range of motion, quality of life and muscle strength, for osteoarthritic patients following elective primary total hip arthroplasty. Methods: Design: Systematic review, using the Cochrane Collaboration Handbook for Systematic Reviews of Interventions and the Quorom Statement. Database searches: AMED, CINAHL, EMBASE, KingsFund, MEDLINE, Cochrane library (Cochrane reviews, Cochrane Central Register of Controlled Trials, DARE), PEDro, The Department of Health National Research Register. Handsearches: Physiotherapy, Physical Therapy, Journal of Bone and Joint Surgery (Britain) Conference Proceedings. No language restrictions were applied. Selection: Trials comparing physiotherapy exercise versus usual/standard care, or comparing two types of relevant exercise physiotherapy, following discharge from hospital after elective primary total hip replacement for osteoarthritis were reviewed. Outcomes: Functional activities of daily living, walking, quality of life, muscle strength and range of hip joint motion. Trial quality was extensively evaluated. Narrative synthesis plus meta-analytic summaries were performed to summarise the data. Results: 8 trials were identified. Trial quality was mixed. Generally poor trial quality, quantity and diversity prevented explanatory meta-analyses. The results were synthesised and meta-analytic summaries were used where possible to provide a formal summary of results. Results indicate that physiotherapy exercise after discharge following total hip replacement has the potential to benefit patients. Conclusion: Insufficient evidence exists to establish the effectiveness of physiotherapy exercise following primary hip replacement for osteoarthritis. Further well designed trials are required to determine the value of post discharge exercise following this increasingly common surgical procedure

On the Polynomial Measurement Error Model

This paper discusses point estimation of the coefficients of polynomial measurement error (errors-in-variables) models. This includes functional and structural models. The connection between these models and total least squares (TLS) is also examined. A compendium of existing as well as new results is presented

On the choice of the update strength in estimation-of-distribution algorithms and ant colony optimization

Probabilistic model-building Genetic Algorithms (PMBGAs) are a class of metaheuristics that evolve probability distributions favoring optimal solutions in the underlying search space by repeatedly sampling from the distribution and updating it according to promising samples. We provide a rigorous runtime analysis concerning the update strength, a vital parameter in PMBGAs such as the step size 1 / K in the so-called compact Genetic Algorithm (cGA) and the evaporation factor ρ in ant colony optimizers (ACO). While a large update strength is desirable for exploitation, there is a general trade-off: too strong updates can lead to unstable behavior and possibly poor performance. We demonstrate this trade-off for the cGA and a simple ACO algorithm on the well-known OneMax function. More precisely, we obtain lower bounds on the expected runtime of Ω(Kn−−√+nlogn) and Ω(n−−√/ρ+nlogn), respectively, suggesting that the update strength should be limited to 1/K,ρ=O(1/(n−−√logn)). In fact, choosing 1/K,ρ∼1/(n−−√logn) both algorithms efficiently optimize OneMax in expected time Θ(nlogn). Our analyses provide new insights into the stochastic behavior of PMBGAs and propose new guidelines for setting the update strength in global optimization

Meta-analysis: Neither quick nor easy

BACKGROUND: Meta-analysis is often considered to be a simple way to summarize the existing literature. In this paper we describe how a meta-analysis resembles a conventional study, requiring a written protocol with design elements that parallel those of a record review. METHODS: The paper provides a structure for creating a meta-analysis protocol. Some guidelines for measurement of the quality of papers are given. A brief overview of statistical considerations is included. Four papers are reviewed as examples. The examples generally followed the guidelines we specify in reporting the studies and results, but in some of the papers there was insufficient information on the meta-analysis process. CONCLUSIONS: Meta-analysis can be a very useful method to summarize data across many studies, but it requires careful thought, planning and implementation

Effects of psychological and psychosocial interventions on sport performance:a meta-analysis

Background: Psychologists are increasingly supporting the quest for performance enhancement in sport and there is a need to evaluate the evidence base underpinning their work. Objectives: To synthesize the most rigorous available research that has evaluated psychological, social, and psychosocial interventions with sport performers on variables relating to their athletic performance, and to address some of the perplexing issues in the sport psychology intervention literature (e.g., do interventions have a lasting effect on sport performance?). Methods: Randomized controlled trials were identified through electronic databases, hand-searching volumes of pertinent journals, scrutinizing reference lists of previous reviews, and contacting experts in the evaluation of interventions in this field. Included studies were required to evaluate the effects of psychological, social, or psychosocial interventions on sport performance in athletes when compared to a no-treatment or placebo-controlled treatment comparison group. A random effects meta-analysis calculating the standardized mean difference (Hedges’ g), meta-regressions, and trim and fill analyses were conducted. Data were analyzed at post-test and follow-up (ranging from 1 to 4 weeks after the intervention finished) assessments. Results: Psychological and psychosocial interventions were shown to enhance sport performance at post-test (k = 35, n = 997, Hedges’ g = 0.57, 95 % CI = 0.22–0.92) and follow-up assessments (k = 8, n = 189, Hedges’ g = 1.16, 95 % CI = 0.25–2.08); no social interventions were included or evaluated. Larger effects were found for psychosocial interventions and there was some evidence that effects were greatest in coach-delivered interventions and in samples with a greater proportion of male participants. Conclusions: Psychological and psychosocial interventions have a moderate positive effect on sport performance, and this effect may last at least a month following the end of the intervention. Future research would benefit from following guidelines for intervention reporting