In particular, it aggregates multiple sub-models called experts based on a gating network. Here, experts can be formulated as neural networks, and they specialize in different aspects of the data.

Specifically, we investigate two cases of such systems.

However, for real-world data, it is very unlikely for the process noise to be perfectly Gaussian. Nonstationarity seems to be prominent in many kinds of temporal data.

Specifically, we investigate two cases of such systems.

We show that the conditions derived for both types of SDEs are generic.

"NIPS 2013 Neural Information Processing Systems December 5 - 10, Lake Tahoe, Nevada, USA",,, "Paper ID:","1009" "Title:","When Are Overcomplete Topic Models Identifiable? First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper gives a sufficient condition for a unique recovery of topic-word matrix of n-persistent overcomplete topic models by a tensor decomposition of moments. In the overcomplete regime, the number of topics are more than that of words. Thus, it is impossible to uniquely recover the relation between topics and words.

Bayesian Additive Regression Trees (BART) is a powerful statistical model that leverages the strengths of Bayesian inference and regression trees. It has received significant attention for capturing complex non-linear relationships and interactions among predictors. However, the accuracy of BART often comes at the cost of interpretability. To address this limitation, we propose ANOVA Bayesian Additive Regression Trees (ANOVA-BART), a novel extension of BART based on the functional ANOVA decomposition, which is used to decompose the variability of a function into different interactions, each representing the contribution of a different set of covariates or factors. Our proposed ANOVA-BART enhances interpretability, preserves and extends the theoretical guarantees of BART, and achieves superior predictive performance. Specifically, we establish that the posterior concentration rate of ANOVA-BART is nearly minimax optimal, and further provides the same convergence rates for each interaction that are not available for BART. Moreover, comprehensive experiments confirm that ANOVA-BART surpasses BART in both accuracy and uncertainty quantification, while also demonstrating its effectiveness in component selection. These results suggest that ANOVA-BART offers a compelling alternative to BART by balancing predictive accuracy, interpretability, and theoretical consistency.

However, for real-world data, it is very unlikely for the process noise to be perfectly Gaussian. Nonstationarity seems to be prominent in many kinds of temporal data.