We introduce Mira, a sample-based score for assessing the accuracy of a candidate conditional distribution using only joint samples from the true data-generating process. Relying on the principle that distributions coincide if they assign equal probability mass to all regions, we derive an analytic expression for the Mira statistic, whose average defines the Mira score. This formulation further allows us to compute theoretical reference values and uncertainty estimates when the candidate distribution matches the true one. This framework enables model comparison by quantifying the alignment between the conditional distribution of a candidate model and the true data generating process. Consequently, Mira enables Bayesian model comparison through direct posterior validation, bypassing the challenging evidence computation. We demonstrate its effectiveness across several toy problems and Bayesian inference tasks.

Plugging back in (11) yields the ideal result.

The authors identify a strategy for compensating agents to disclose private and relevant data. The strategy draws on interesting ideas from the machine learning literature, including the use of the stochastic gradient descent algorithm to set the payment for the data. This allows effective compensation of agents while maintaining a limited budget. The authors also include mechanisms for preserving the privacy of agents, and identification of different "profit maximizing" strategies for agent to select given their confidence in their data. It appears that the substantive contribution is in identifying a mechanism that compensates agents for their data while maintaing a bounded budget.

We use Fourier Neural Operators (FNOs) to study the relation between the modulus and phase of amplitudes in $2\to 2$ elastic scattering at fixed energies. Unlike previous approaches, we do not employ the integral relation imposed by unitarity, but instead train FNOs to discover it from many samples of amplitudes with finite partial wave expansions. When trained only on true samples, the FNO correctly predicts (unique or ambiguous) phases of amplitudes with infinite partial wave expansions. When also trained on false samples, it can rate the quality of its prediction by producing a true/false classifying index. We observe that the value of this index is strongly correlated with the violation of the unitarity constraint for the predicted phase, and present examples where it delineates the boundary between allowed and disallowed profiles of the modulus. Our application of FNOs is unconventional: it involves a simultaneous regression-classification task and emphasizes the role of statistics in ensembles of NOs. We comment on the merits and limitations of the approach and its potential as a new methodology in Theoretical Physics.

But first, what is a confusion matrix? In machine learning, a confusion matrix is a kind-of confusing table used to understand how well our model predictions perform(especially confusing when we have multiple classes and not the classic binary 0/1 problems). However, gradually I figured out that the confusion-matrix is not so confusing and helps me a ton in understanding the model behaviour and interpreting the results. So I'm going to try to do the same here.. make it less confusing, more interesting and easier to interpret! The columns represent predictions made by our model and the rows represent the actual classes(this is the format of the very popular Python library for ML: sklearn.

Deep generative models are generally categorized into explicit models and implicit models. The former defines an explicit density form, whose normalizing constant is often unknown; while the latter, including generative adversarial networks (GANs), generates samples without explicitly defining a density function. In spite of substantial recent advances demonstrating the power of the two classes of generative models in many applications, both of them, when used alone, suffer from respective limitations and drawbacks. To mitigate these issues, we propose Stein Bridging, a novel joint training framework that connects an explicit density estimator and an implicit sample generator with Stein discrepancy. We show that the Stein Bridge induces new regularization schemes for both explicit and implicit models. Convergence analysis and extensive experiments demonstrate that the Stein Bridging i) improves the stability and sample quality of the GAN training, and ii) facilitates the density estimator to seek more modes in data and alleviate the mode-collapse issue. Additionally, we discuss several applications of Stein Bridging and useful tricks in practical implementation used in our experiments.