ABCDP: Approximate Bayesian Computation with Differential Privacy.

We developed a novel approximate Bayesian computation (ABC) framework, ABCDP, which produces differentially private (DP) and approximate posterior samples. Our framework takes advantage of the sparse vector technique (SVT), widely studied in the differential privacy literature. SVT incurs the privacy cost only when a condition (whether a quantity of interest is above/below a threshold) is met. If the condition is sparsely met during the repeated queries, SVT can drastically reduce the cumulative privacy loss, unlike the usual case where every query incurs the privacy loss. In ABC, the quantity of interest is the distance between observed and simulated data, and only when the distance is below a threshold can we take the corresponding prior sample as a posterior sample. Hence, applying SVT to ABC is an organic way to transform an ABC algorithm to a privacy-preserving variant with minimal modification, but yields the posterior samples with a high privacy level. We theoretically analyzed the interplay between the noise added for privacy and the accuracy of the posterior samples. We apply ABCDP to several data simulators and show the efficacy of the proposed framework.

Cognitive Bias in Ambiguity Judgements: Using Computational Models to Dissect the Effects of Mild Mood Manipulation in Humans.

Positive and negative moods can be treated as prior expectations over future delivery of rewards and punishments. This provides an inferential foundation for the cognitive (judgement) bias task, now widely-used for assessing affective states in non-human animals. In the task, information about affect is extracted from the optimistic or pessimistic manner in which participants resolve ambiguities in sensory input. Here, we report a novel variant of the task aimed at dissecting the effects of affect manipulations on perceptual and value computations for decision-making under ambiguity in humans. Participants were instructed to judge which way a Gabor patch (250ms presentation) was leaning. If the stimulus leant one way (e.g. left), pressing the REWard key yielded a monetary WIN whilst pressing the SAFE key failed to acquire the WIN. If it leant the other way (e.g. right), pressing the SAFE key avoided a LOSS whilst pressing the REWard key incurred the LOSS. The size (0-100 UK pence) of the offered WIN and threatened LOSS, and the ambiguity of the stimulus (vertical being completely ambiguous) were varied on a trial-by-trial basis, allowing us to investigate how decisions were affected by differing combinations of these factors. Half the subjects performed the task in a 'Pleasantly' decorated room and were given a gift (bag of sweets) prior to starting, whilst the other half were in a bare 'Unpleasant' room and were not given anything. Although these treatments had little effect on self-reported mood, they did lead to differences in decision-making. All subjects were risk averse under ambiguity, consistent with the notion of loss aversion. Analysis using a Bayesian decision model indicated that Unpleasant Room subjects were ('pessimistically') biased towards choosing the SAFE key under ambiguity, but also weighed WINS more heavily than LOSSes compared to Pleasant Room subjects. These apparently contradictory findings may be explained by the influence of affect on different processes underlying decision-making, and the task presented here offers opportunities for further dissecting such processes.

High-dimensional feature selection by feature-wise kernelized Lasso.

The goal of supervised feature selection is to find a subset of input features that are responsible for predicting output values. The least absolute shrinkage and selection operator (Lasso) allows computationally efficient feature selection based on linear dependency between input features and output values. In this letter, we consider a feature-wise kernelized Lasso for capturing nonlinear input-output dependency. We first show that with particular choices of kernel functions, nonredundant features with strong statistical dependence on output values can be found in terms of kernel-based independence measures such as the Hilbert-Schmidt independence criterion. We then show that the globally optimal solution can be efficiently computed; this makes the approach scalable to high-dimensional problems. The effectiveness of the proposed method is demonstrated through feature selection experiments for classification and regression with thousands of features.