We present a sound and strongly complete axiomatization of a reasoning about linear combinations of conditional probabilities, including comparative statements. The developed logic is decidable, with a PSPACE containment for the decision procedure.

Deep Neural Networks trained as image auto-encoders have recently emerged as a promising direction for advancing the state of the art in image compression. The key challenge in learning such networks is twofold: to deal with quantization, and to control the trade-off between reconstruction error (distortion) and entropy (rate) of the latent image representation. In this paper, we focus on the l...

Semantic coherence is a higher-order coherence benchmark that assesses whether a constellation of estimates--P(A), P(B), P(B | A), and P(A | B)--maps onto the relationship between sets implied by the description of a given problem. We present an automated method for evaluating semantic coherence in conditional probability estimates that efficiently reduces a large problem space into five meanin...

Many regression schemes deliver a point estimate only, but often it is useful or even essential to quantify the uncertainty inherent in a prediction. If a conditional density estimate is available, then prediction intervals can be derived from it. In this paper we compare three techniques for computing conditional density estimates using a class probability estimator, where this estimator is ap...

CPTtools-package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 ACED.scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 areaProbs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 betaci . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 buildFactorTa...

1 Last two lectures ¯ probability spaces ¯ probability measure ¯ random variables and stochastic processes ¯ distribution functions ¯ independence ¯ conditional probability ¯ memoriless property of geometric and exponential distributions ¯ expectation ¯ conditional expectation (double expectation) ¯ mean-square estimation 1

We define a new notion of conditional belief, which plays the same role for Dempster­ Shafer belief functions as conditional probability does for probability functions. Our definition is dif­ ferent from the standard definition given by Demp­ ster, and avoids many of the well-known problems of that definition. Just as the conditional prob­ ability Pr(·IB) is a probability function which is the ...

This paper introduces a new type of R&D subsidy, which is conditional on the success of the R&D project. In a threestage model, the government chooses a subsidy(ies) in the first stage; in the second stage, a monopolist chooses R&D effort which determines the size or the probability of success of the R&D project; in the last stage, the firm chooses its output. It is found that conditional subsi...

In the first part, we recall the pure and simple notion of the truth-functional (alias material) conditional proposition, and then how it can occur in combination with other elements, creating more complex kinds of conditional assertion. We discuss the subtle distinction between conditional probability and the probability of a conditional. Finally, we explain the notion of a counterfactual cond...