Active Bayesian Optimization: Minimizing Minimizer Entropy

The ultimate goal of optimization is to find the minimizer of a target function.However, typical criteria for active optimization often ignore the uncertainty about the minimizer. We propose a novel criterion for global optimization and an associated sequential active learning strategy using Gaussian processes.Our criterion is the reduction of uncertainty in the posterior distribution of the function minimizer. It can also flexibly incorporate multiple global minimizers. We implement a tractable approximation of the criterion and demonstrate that it obtains the global minimizer accurately compared to conventional Bayesian optimization criteria

Korean sibling caregivers of individuals diagnosed with schizophrenia

Siblings of individuals diagnosed with schizophrenia are an important source of family caregiving. Unfortunately, limited information is available about sibling caregivers because existing studies have focused on other family relationships such as parents, spouses, and children. To fill the knowledge gap, the purpose of this study is to describe Korean sibling caregivers’ experience with individuals diagnosed with schizophrenia. Guided by Colaizzi’s descriptive phenomenological methodology, we conducted in-depth, semi-structured, face-to-face interviews with eight individuals who have a sibling (1) diagnosed with schizophrenia and (2) hospitalized in an inpatient psychiatric unit. We discerned six key themes: sorrow, burnout, shame, different perspectives in life, acceptance, and responsibility. We categorized these themes into three groups: suffering, hope, and responsibility and obligation. Sibling caregivers of individuals with schizophrenia experience a mixture of several emotions. Participants loved their brother or sister with schizophrenia, but at the same time they felt shame and fear. While they were burdened by the responsibilities of caregiving, they remained loyal to their sibling with schizophrenia, continuing to help their siblings reach their full potential. Although participants were confused about the symptoms of schizophrenia, they were committed to learning more about the illness. Because we conducted the current study in Korea, the findings of this study may be unique to Korea culture. Further studies are needed to compare and contrast nuanced differences in sibling caregivers’ experience among different cultural groups

Household Size, Home Health Care, and Medical Expenditures

We document a robust negative correlation in which residing in a larger family is associated with lower consumption of medical care ceteris paribus. For men, an additional household member is associated with between $659.69 and$1039.97 fewer expenditures on health care and, for women, the estimates range between $391.28 and$728.66. Using quantile regression, the magnitude of the coefficients on household size increases monotonically with the quantile of medical expenditure. If household size is a proxy for home health care then these results suggest that home health care substitutes for medical care obtained on the market and that the degree of substitution increases with one's consumption of medical care and by implication decreases with one's health status. Finally, we provide suggestive evidence that the relative generosity of coverage for home health care by MEDICARE vis-a-vis private insurance may induce a crowdout of family care-giving by home care obtained through professional agencies.household size, medical expenditure, family, care-giving

K2-ABC: Approximate Bayesian Computation with Kernel Embeddings

Complicated generative models often result in a situation where computing the likelihood of observed data is intractable, while simulating from the conditional density given a parameter value is relatively easy. Approximate Bayesian Computation (ABC) is a paradigm that enables simulation-based posterior inference in such cases by measuring the similarity between simulated and observed data in terms of a chosen set of summary statistics. However, there is no general rule to construct sufficient summary statistics for complex models. Insufficient summary statistics will "leak" information, which leads to ABC algorithms yielding samples from an incorrect (partial) posterior. In this paper, we propose a fully nonparametric ABC paradigm which circumvents the need for manually selecting summary statistics. Our approach, K2-ABC, uses maximum mean discrepancy (MMD) as a dissimilarity measure between the distributions over observed and simulated data. MMD is easily estimated as the squared difference between their empirical kernel embeddings. Experiments on a simulated scenario and a real-world biological problem illustrate the effectiveness of the proposed algorithm

Differentially private stochastic expectation propagation (DP-SEP)

We are interested in privatizing an approximate posterior inference algorithm called Expectation Propagation (EP). EP approximates the posterior by iteratively refining approximations to the local likelihoods, and is known to provide better posterior uncertainties than those by variational inference (VI). However, EP needs a large memory to maintain all local approximates associated with each datapoint in the training data. To overcome this challenge, stochastic expectation propagation (SEP) considers a single unique local factor that captures the average effect of each likelihood term to the posterior and refines it in a way analogous to EP. In terms of privacy, SEP is more tractable than EP because at each refining step of a factor, the remaining factors are fixed and do not depend on other datapoints as in EP, which makes the sensitivity analysis straightforward. We provide a theoretical analysis of the privacy-accuracy trade-off in the posterior estimates under our method, called differentially private stochastic expectation propagation (DP-SEP). Furthermore, we demonstrate the performance of our DP-SEP algorithm evaluated on both synthetic and real-world datasets in terms of the quality of posterior estimates at different levels of guaranteed privacy