Mixture Selection, Mechanism Design, and Signaling

We pose and study a fundamental algorithmic problem which we term mixture selection, arising as a building block in a number of game-theoretic applications: Given a function $g$ from the $n$-dimensional hypercube to the bounded interval $[-1,1]$, and an $n \times m$ matrix $A$ with bounded entries, maximize $g(Ax)$ over $x$ in the $m$-dimensional simplex. This problem arises naturally when one seeks to design a lottery over items for sale in an auction, or craft the posterior beliefs for agents in a Bayesian game through the provision of information (a.k.a. signaling). We present an approximation algorithm for this problem when $g$ simultaneously satisfies two smoothness properties: Lipschitz continuity with respect to the $L^\infty$ norm, and noise stability. The latter notion, which we define and cater to our setting, controls the degree to which low-probability errors in the inputs of $g$ can impact its output. When $g$ is both $O(1)$-Lipschitz continuous and $O(1)$-stable, we obtain an (additive) PTAS for mixture selection. We also show that neither assumption suffices by itself for an additive PTAS, and both assumptions together do not suffice for an additive FPTAS. We apply our algorithm to different game-theoretic applications from mechanism design and optimal signaling. We make progress on a number of open problems suggested in prior work by easily reducing them to mixture selection: we resolve an important special case of the small-menu lottery design problem posed by Dughmi, Han, and Nisan; we resolve the problem of revenue-maximizing signaling in Bayesian second-price auctions posed by Emek et al. and Miltersen and Sheffet; we design a quasipolynomial-time approximation scheme for the optimal signaling problem in normal form games suggested by Dughmi; and we design an approximation algorithm for the optimal signaling problem in the voting model of Alonso and C\^{a}mara

Signaling in Quasipolynomial time

Strategic interactions often take place in an environment rife with uncertainty. As a result, the equilibrium of a game is intimately related to the information available to its players. The \emph{signaling problem} abstracts the task faced by an informed "market maker", who must choose how to reveal information in order to effect a desirable equilibrium. In this paper, we consider two fundamental signaling problems: one for abstract normal form games, and the other for single item auctions. For the former, we consider an abstract class of objective functions which includes the social welfare and weighted combinations of players' utilities, and for the latter we restrict our attention to the social welfare objective and to signaling schemes which are constrained in the number of signals used. For both problems, we design approximation algorithms for the signaling problem which run in quasi-polynomial time under various conditions, extending and complementing the results of various recent works on the topic. Underlying each of our results is a "meshing scheme" which effectively overcomes the "curse of dimensionality" and discretizes the space of "essentially different" posterior beliefs -- in the sense of inducing "essentially different" equilibria. This is combined with an algorithm for optimally assembling a signaling scheme as a convex combination of such beliefs. For the normal form game setting, the meshing scheme leads to a convex partition of the space of posterior beliefs and this assembly procedure is reduced to a linear program, and in the auction setting the assembly procedure is reduced to submodular function maximization

The relationship of asthma and the pattern of adiposity in adult Chinese

Poster presentationpublished_or_final_versionThe 15th Medical Research Conference, Department of Medicine, The University of Hong Kong, Hong Kong, 16 January 2010. In Hong Kong Medical Journal, 2010, v. 16, suppl. 1, p. 56, abstract no. 9

PLASER: Pronunciation Learning via Automatic Speech Recognition

PLASER is a multimedia tool with instant feedback designed to teach English pronunciation for high-school students of Hong Kong whose mother tongue is Cantonese Chinese. The objective is to teach correct pronunciation and not to assess a student's overall pronunciation quality. Major challenges related to speech recognition technology include: allowance for non-native accent, reliable and corrective feedbacks, and visualization of errors

Hong Kong dentists' preparedness for medical emergency in dental clinics

Aim: The aim of this study was to investigate the Hong Kong dentists’ and dental clinics’ preparedness for medical emergency in the dental clinic. Methods: Two custom designed questionnaires were developed, one for dentists and another for dental clinics, to collect the required information. The sampling frame for participants was the list of registered dentists published by the Hong Kong Dental Council on its website in January 2016. A total of 434 dentists and 143 dental clinics were selected from the list by systematic random sampling. The latter sample was supplemented by 10 randomly selected government dental clinics. The questionnaires were mailed the selected dentists together with a cover letter and a stamped return envelope. A reminder letter and another copy of the questionnaire were sent out two weeks after the first mailing. Results: 167 (38%) completed dentist questionnaires and 53 (35%) clinic questionnaires were collected. Most of the respondent dentists had some deficient knowledge on basic life support (BLS), their mean score was 3.5 out of a maximum of 5. Most (>60%) of the respondents thought they were competent in performing medical emergency procedures except giving intravenous injection. Moreover, most (>60%) of them held positive attitude towards having immediate availability of essential medical emergency equipment and drugs in their clinic. Dentists who were more recent graduates, those with postgraduate qualifications, and those who work with accompaniment generally had higher mean BLS knowledge scores. In the dental clinics, the most commonly kept medical emergency equipment/drug was instant glucose (70%) and followed by antihistamine (62%). Only a quarter of the clinics were equipped with AED, and 45% were equipped with oxygen cylinder. For 8 out of the 11 items, a higher proportion of the bigger clinics (>2 dental chairs) than the smaller clinics had the medical emergency equipment/drug available (Chi-square test, p<0.05). Conclusion: Hong Kong dentists have a moderate level of knowledge on BLS which should be enhanced through regular attendance at CE courses. Their knowledge level is affected by a number of their background and professional activities factors. Most dental clinics in Hong Kong have only few of the essential medical emergency equipment and drugs while the larger clinics are better equipped than the smaller clinics.published_or_final_versio

Elevated plasma TGF-β1 levels in patients with chronic obstructive pulmonary disease

SummaryBackgroundTransforming growth factor-β1 (TGF-β1), a multifunctional cytokine, has been implicated to be responsible for the increased deposition of extracellular matrix in the airways, and increased submucosal collagen expression in chronic obstructive pulmonary disease (COPD). We determined plasma TGF-β1 levels in patients with COPD and explored its association with common functional polymorphisms of TGF-β1 gene at C-509T and T869C in the development of COPD in a case–control study.MethodsStable COPD patients who were ever smokers, and age and pack-years smoked matched healthy controls (n = 205 in each group) were recruited for measurement of plasma TGF-β1 levels using commercially available ELISA kit, and genotyped at C-509T and T869C functional polymorphisms of TGF-β1 gene using polymerase chain reaction and restriction fragment length polymorphism (PCR–RFLP).ResultsCOPD patients had significantly elevated plasma TGF-β1 levels in comparison to healthy controls irrespective of the genotypes. Allele frequencies and genotype distributions at both polymorphic sites were not different among COPD patients or controls. TGF-β1 levels were inversely correlated (Pearson's correlation analysis) with FEV1 (% predicted) (p < 0.001) and FVC (% predicted) (p < 0.001).ConclusionThe findings of elevated plasma TGF-β1 levels in patients with COPD suggest that TGF-β1 may play a role in COPD pathogenesis. The C-509T and T869C functional polymorphisms of TGF-β1 gene do not represent a genetic predisposition to COPD susceptibility in Hong Kong Chinese patients

A cluster of cases of severe acute respiratory syndrome in Hong Kong

BACKGROUND: Information on the clinical features of the severe acute respiratory syndrome (SARS) will be of value to physicians caring for patients suspected of having this disorder. METHODS: We abstracted data on the clinical presentation and course of disease in 10 epidemiologically linked Chinese patients (5 men and 5 women 38 to 72 years old) in whom SARS was diagnosed between February 22, 2003, and March 22, 2003, at our hospitals in Hong Kong, China. RESULTS: Exposure between the source patient and subsequent patients ranged from minimal to that between patient and health care provider. The incubation period ranged from 2 to 11 days. All patients presented with fever (temperature, >38°C for over 24 hours), and most presented with rigor, dry cough, dyspnea, malaise, headache, and hypoxemia. Physical examination of the chest revealed crackles and percussion dullness. Lymphopenia was observed in nine patients, and most patients had mildly elevated aminotransferase levels but normal serum creatinine levels. Serial chest radiographs showed progressive air-space disease. Two patients died of progressive respiratory failure; histologic analysis of their lungs showed diffuse alveolar damage. There was no evidence of infection by Mycoplasma pneumoniae, Chlamydia pneumoniae, or Legionella pneumophila. All patients received corticosteroid and ribavirin therapy a mean (±SD) of 9.6±5.42 days after the onset of symptoms, and eight were treated earlier with a combination of beta-lactams and macrolide for 4±1.9 days, with no clinical or radiologic efficacy. CONCLUSIONS: SARS appears to be infectious in origin. Fever followed by rapidly progressive respiratory compromise is the key complex of signs and symptoms from which the syndrome derives its name. The microbiologic origins of SARS remain unclear.published_or_final_versio