Ultimately, machine learning models are used to make decisions.

Neural Information Processing Systems http://nips.cc/

The degree of confidence in one's choice or decision is a critical aspect of perceptual decision making. Attempts to quantify a decision maker's confidence by measuring accuracy in a task have yielded limited success because confidence and accuracy are typically not equal. In this paper, we introduce a Bayesian framework to model confidence in perceptual decision making. We show that this model, based on partially observable Markov decision processes (POMDPs), is able to predict confidence of a decision maker based only on the data available to the experimenter. We test our model on two experiments on confidence-based decision making involving the well-known random dots motion discrimination task. In both experiments, we show that our model's predictions closely match experimental data. Additionally, our model is also consistent with other phenomena such as the hard-easy effect in perceptual decision making.

A market scoring rule (MSR) - a popular tool for designing algorithmic prediction markets - is an incentive-compatible mechanism for the aggregation of probabilistic beliefs from myopic risk-neutral agents. In this paper, we add to a growing body of research aimed at understanding the precise manner in which the price process induced by a MSR incorporates private information from agents who deviate from the assumption of risk-neutrality. We first establish that, for a myopic trading agent with a risk-averse utility function, a MSR satisfying mild regularity conditions elicits the agent's risk-neutral probability conditional on the latest market state rather than her true subjective probability. Hence, we show that a MSR under these conditions effectively behaves like a more traditional method of belief aggregation, namely an opinion pool, for agents' true probabilities.

Many real datasets are hierarchically structured.

We present a method for learning Bayesian networks from data sets containing thousands of variables without the need for structure constraints. Our approach is made of two parts. The first is a novel algorithm that effectively explores the space of possible parent sets of a node. It guides the exploration towards the most promising parent sets on the basis of an approximated score function that is computed in constant time. The second part is an improvement of an existing ordering-based algorithm for structure optimization. The new algorithm provably achieves a higher score compared to its original formulation. Our novel approach consistently outperforms the state of the art on very large data sets.

We show that the maximum-likelihood (ML) estimate of models derived from Luce's choice axiom (e.g., the Plackett-Luce model) can be expressed as the

Here we describe CGS in more details. Eqn. 10 we obtain: null null Expression under the last integral in Eqn. 13 is tractable, thanks to the conjugacy of the Normal-inverse-Wishart prior to the Gaussian likelihood. Finally, posterior predictive density (10) can be written as a mixture of multivariate Student's CIFAR experiments used the standard train/test split. Results for architectures not included in Section 4 are summarized in Fig. C.1. Table C.1: CNN architectures used in experiments (Section 4).

In this paper, we propose a game-theoretic framework for studying attacks and defenses which exist in equilibrium.