Distribution shift (DS) may have two levels: the distribution itself changes, and the support (i.e., the set where the probability density is non-zero) also changes.

Distribution shift (DS) may have two levels: the distribution itself changes, and the support (i.e., the set where the probability density is non-zero) also changes.

Recent studies have increasingly focused on non-asymptotic convergence analyses for actor-critic (AC) algorithms. One such effort introduced a two-timescale critic-actor algorithm for the discounted cost setting using a tabular representation, where the usual roles of the actor and critic are reversed. However, only asymptotic convergence was established there. Subsequently, both asymptotic and non-asymptotic analyses of the critic-actor algorithm with linear function approximation were conducted. In our work, we introduce the first natural critic-actor algorithm with function approximation for the long-run average cost setting and under inequality constraints. We provide the non-asymptotic convergence guarantees for this algorithm. Our analysis establishes optimal learning rates and we also propose a modification to enhance sample complexity. We further show the results of experiments on three different Safety-Gym environments where our algorithm is found to be competitive in comparison with other well known algorithms.

Next, we will show that e ( x, S) is sub-exponential. Proposition 3. Let g = g ( x, U), and fix In Section 2.3 of [ BCCS21 ], it is shown that kr F ( x) r ( x) k p nL + p n We use these facts to show that Gaussian smoothed gradients gives a valid first order oracle. First, by the triangle inequality, we have k g ( x, U) r ( x) k k g ( x, U) r F ( x) k + kr F ( x) r ( x) k . To prove Lemma 2, we will first prove two additional lemmas. The first lemma shows that the number of large and successful iterations is bounded below by the number of large and unsuccessful ones up to a constant.

Transformers have achieved remarkable success in tabular data generation. However, they lack domain-specific inductive biases which are critical to preserving the intrinsic characteristics of tabular data. Meanwhile, they suffer from poor scalability and efficiency due to quadratic computational complexity. In this paper, we propose TabTreeFormer, a hybrid transformer architecture that incorporates a tree-based model that retains tabular-specific inductive biases of non-smooth and potentially low-correlated patterns caused by discreteness and non-rotational invariance, and hence enhances the fidelity and utility of synthetic data. In addition, we devise a dual-quantization tokenizer to capture the multimodal continuous distribution and further facilitate the learning of numerical value distribution. Moreover, our proposed tokenizer reduces the vocabulary size and sequence length due to the limited complexity (e.g., dimension-wise semantic meaning) of tabular data, rendering a significant model size shrink without sacrificing the capability of the transformer model. We evaluate TabTreeFormer on 10 datasets against multiple generative models on various metrics; our experimental results show that TabTreeFormer achieves superior fidelity, utility, privacy, and efficiency. Our best model yields a 40% utility improvement with 1/16 of the baseline model size.

It is crucial to assess the predictive performance of a model in order to establish its practicality and relevance in real-world scenarios, particularly for high-dimensional data analysis. Among data splitting or resampling methods, cross-validation (CV) is extensively used for several tasks such as estimating the prediction error, tuning the regularization parameter, and selecting the most suitable predictive model among competing alternatives. The K-fold cross-validation is a popular CV method but its limitation is that the risk estimates are highly dependent on the partitioning of the data (for training and testing). Here, the issues regarding the reproducibility of the K-fold CV estimator is demonstrated in hypothesis testing wherein different partitions lead to notably disparate conclusions. This study presents an alternative novel predictive performance test and valid confidence intervals based on exhaustive nested cross-validation for determining the difference in prediction error between two model-fitting algorithms. A naive implementation of the exhaustive nested cross-validation is computationally costly. Here, we address concerns regarding computational complexity by devising a computationally tractable closed-form expression for the proposed cross-validation estimator using ridge regularization. Our study also investigates strategies aimed at enhancing statistical power within high-dimensional scenarios while controlling the Type I error rate. To illustrate the practical utility of our method, we apply it to an RNA sequencing study and demonstrate its effectiveness in the context of biological data analysis.

The standard state-of-the-art backend for text-independent speaker recognizers that use i-vectors or x-vectors, is Gaussian PLDA (G-PLDA), assisted by a Gaussianization step involving length normalization. G-PLDA can be trained with both generative or discriminative methods. It has long been known that heavy-tailed PLDA (HT-PLDA), applied without length normalization, gives similar accuracy, but at considerable extra computational cost. We have recently introduced a fast scoring algorithm for a discriminatively trained HT-PLDA backend. This paper extends that work by introducing a fast, variational Bayes, generative training algorithm. We compare old and new backends, with and without length-normalization, with i-vectors and x-vectors, on SRE'10, SRE'16 and SITW.