The Power of an Example: Hidden Set Size Approximation Using Group Queries and Conditional Sampling

We study a basic problem of approximating the size of an unknown set $S$ in a known universe $U$. We consider two versions of the problem. In both versions the algorithm can specify subsets $T\subseteq U$. In the first version, which we refer to as the group query or subset query version, the algorithm is told whether $T\cap S$ is non-empty. In the second version, which we refer to as the subset sampling version, if $T\cap S$ is non-empty, then the algorithm receives a uniformly selected element from $T\cap S$. We study the difference between these two versions under different conditions on the subsets that the algorithm may query/sample, and in both the case that the algorithm is adaptive and the case where it is non-adaptive. In particular we focus on a natural family of allowed subsets, which correspond to intervals, as well as variants of this family

Adaptive Probability Theory: Human Biases as an Adaptation

Humans make mistakes in our decision-making and probability judgments. While the heuristics used for decision-making have been explained as adaptations that are both efficient and fast, the reasons why people deal with probabilities using the reported biases have not been clear. We will see that some of these biases can be understood as heuristics developed to explain a complex world when little information is available. That is, they approximate Bayesian inferences for situations more complex than the ones in laboratory experiments and in this sense might have appeared as an adaptation to those situations. When ideas as uncertainty and limited sample sizes are included in the problem, the correct probabilities are changed to values close to the observed behavior. These ideas will be used to explain the observed weight functions, the violations of coalescing and stochastic dominance reported in the literature

Standard survey methods for estimating colony losses and explanatory risk factors in Apis mellifera

This chapter addresses survey methodology and questionnaire design for the collection of data pertaining to estimation of honey bee colony loss rates and identification of risk factors for colony loss. Sources of error in surveys are described. Advantages and disadvantages of different random and non-random sampling strategies and different modes of data collection are presented to enable the researcher to make an informed choice. We discuss survey and questionnaire methodology in some detail, for the purpose of raising awareness of issues to be considered during the survey design stage in order to minimise error and bias in the results. Aspects of survey design are illustrated using surveys in Scotland. Part of a standardized questionnaire is given as a further example, developed by the COLOSS working group for Monitoring and Diagnosis. Approaches to data analysis are described, focussing on estimation of loss rates. Dutch monitoring data from 2012 were used for an example of a statistical analysis with the public domain R software. We demonstrate the estimation of the overall proportion of losses and corresponding confidence interval using a quasi-binomial model to account for extra-binomial variation. We also illustrate generalized linear model fitting when incorporating a single risk factor, and derivation of relevant confidence intervals

Improved Bounds for Universal One-Bit Compressive Sensing

Unlike compressive sensing where the measurement outputs are assumed to be real-valued and have infinite precision, in "one-bit compressive sensing", measurements are quantized to one bit, their signs. In this work, we show how to recover the support of sparse high-dimensional vectors in the one-bit compressive sensing framework with an asymptotically near-optimal number of measurements. We also improve the bounds on the number of measurements for approximately recovering vectors from one-bit compressive sensing measurements. Our results are universal, namely the same measurement scheme works simultaneously for all sparse vectors. Our proof of optimality for support recovery is obtained by showing an equivalence between the task of support recovery using 1-bit compressive sensing and a well-studied combinatorial object known as Union Free Families.Comment: 14 page

Interactively Test Driving an Object Detector: Estimating Performance on Unlabeled Data

In this paper, we study the problem of `test-driving' a detector, i.e. allowing a human user to get a quick sense of how well the detector generalizes to their specific requirement. To this end, we present the first system that estimates detector performance interactively without extensive ground truthing using a human in the loop. We approach this as a problem of estimating proportions and show that it is possible to make accurate inferences on the proportion of classes or groups within a large data collection by observing only $5-10\%$ of samples from the data. In estimating the false detections (for precision), the samples are chosen carefully such that the overall characteristics of the data collection are preserved. Next, inspired by its use in estimating disease propagation we apply pooled testing approaches to estimate missed detections (for recall) from the dataset. The estimates thus obtained are close to the ones obtained using ground truth, thus reducing the need for extensive labeling which is expensive and time consuming.Comment: Published at Winter Conference on Applications of Computer Vision, 201