With the complexity of the network structure, uncertainty inference has become an important task to improve classification accuracy for artificial intelligence systems. For image classification tasks, we propose a structured DropConnect (SDC) framework to model the output of a deep neural network by a Dirichlet distribution. We introduce a DropConnect strategy on weights in the fully connected layers during training. In test, we split the network into several sub-networks, and then model the Dirichlet distribution by match its moments with the mean and variance of the outputs of these sub-networks. The entropy of the estimated Dirichlet distribution is finally utilized for uncertainty inference. In this paper, this framework is implemented on LeNet5 and VGG16 models for misclassification detection and out-of-distribution detection on MNIST and CIFAR-10 datasets. Experimental results show that the performance of the proposed SDC can be comparable to other uncertainty inference methods. Furthermore, the SDC is adapted well to different Figure 1: Illustration of the proposed structured DropConnect network structures with certain generalization capabilities and (SDC). In train phase, DropConnect is used on the research prospects.

This paper proposes methods for unsupervised lexical acquisition for relative spatial concepts using spoken user utterances. A robot with a flexible spoken dialog system must be able to acquire linguistic representation and its meaning specific to an environment through interactions with humans as children do. Specifically, relative spatial concepts (e.g., front and right) are widely used in our daily lives, however, it is not obvious which object is a reference object when a robot learns relative spatial concepts. Therefore, we propose methods by which a robot without prior knowledge of words can learn relative spatial concepts. The methods are formulated using a probabilistic model to estimate the proper reference objects and distributions representing concepts simultaneously. The experimental results show that relative spatial concepts and a phoneme sequence representing each concept can be learned under the condition that the robot does not know which located object is the reference object. Additionally, we show that two processes in the proposed method improve the estimation accuracy of the concepts: generating candidate word sequences by class n-gram and selecting word sequences using location information. Furthermore, we show that clues to reference objects improve accuracy even though the number of candidate reference objects increases.

We study learning algorithms for the classical Markovian bandit problem with discount. We explain how to adapt PSRL [24] and UCRL2 [2] to exploit the problem structure. These variants are called MB-PSRL and MB-UCRL2. While the regret bound and runtime of vanilla implementations of PSRL and UCRL2 are exponential in the number of bandits, we show that the episodic regret of MB-PSRL and MB-UCRL2 is $\tilde O(S\sqrt{nK})$ where $K$ is the number of episodes, n is the number of bandits and S is the number of states of each bandit (the exact bound in $S$, $n$ and $K$ is given in the paper). Up to a factor $\sqrt S$, this matches the lower bound of $\Omega(\sqrt{SnK}$) that we also derive in the paper. MB-PSRL is also computationally efficient: its runtime is linear in the number of bandits. We further show that this linear runtime cannot be achieved by adapting classical non-Bayesian algorithms such as UCRL2 or UCBVI to Markovian bandit problems. Finally, we perform numerical experiments that confirm that MB-PSRL outperforms other existing algorithms in practice, both in terms of regret and of computation time.

"For how many days during the past 30 days was your mental health not good?" The responses to this question measure self-reported mental health and can be linked to important covariates in the National Health and Nutrition Examination Survey (NHANES). However, these count variables present major distributional challenges: the data are overdispersed, zero-inflated, bounded by 30, and heaped in five- and seven-day increments. To meet these challenges, we design a semiparametric estimation and inference framework for count data regression. The data-generating process is defined by simultaneously transforming and rounding (STAR) a latent Gaussian regression model. The transformation is estimated nonparametrically and the rounding operator ensures the correct support for the discrete and bounded data. Maximum likelihood estimators are computed using an EM algorithm that is compatible with any continuous data model estimable by least squares. STAR regression includes asymptotic hypothesis testing and confidence intervals, variable selection via information criteria, and customized diagnostics. Simulation studies validate the utility of this framework. STAR is deployed to study the factors associated with self-reported mental health and demonstrates substantial improvements in goodness-of-fit compared to existing count data regression models.

Recent years have witnessed an upsurge of interest in employing flexible machine learning models for instrumental variable (IV) regression, but the development of uncertainty quantification methodology is still lacking. In this work we present a scalable quasi-Bayesian procedure for IV regression, building upon the recently developed kernelized IV models. Contrary to Bayesian modeling for IV, our approach does not require additional assumptions on the data generating process, and leads to a scalable approximate inference algorithm with time cost comparable to the corresponding point estimation methods. Our algorithm can be further extended to work with neural network models. We analyze the theoretical properties of the proposed quasi-posterior, and demonstrate through empirical evaluation the competitive performance of our method.

DN), thus, limiting their use to moderately sized data sets. To enable posterior inference in GPs on large-scale problems, Inspired by recent advances in the field of expertbased recent work (see e.g. Liu et al. [2020] for a detailed approximations of Gaussian processes (GPs), review) mainly resorts to global approximations to the posterior, we present an expert-based approach to large-scale e.g., using inducing points, or local approximations multi-output regression using single-output GP that aim to distribute the computation of the posterior distribution experts. Employing a deeply structured mixture onto local experts. Unfortunately, most of these of single-output GPs encoded via a probabilistic approaches only focus on single-output regression, i.e., the circuit allows us to capture correlations between dependent variable is univariate, and in the case of local multiple output dimensions accurately. By recursively approximations, do not easily extend to multi-output regression partitioning the covariate space and the output tasks, see Bruinsma et al. [2020] for a detailed space, posterior inference in our model reduces to discussion on recent techniques on multi-output GPs.

Imitation learning enables high-fidelity, vision-based learning of policies within rich, photorealistic environments. However, such techniques often rely on traditional discrete-time neural models and face difficulties in generalizing to domain shifts by failing to account for the causal relationships between the agent and the environment. In this paper, we propose a theoretical and experimental framework for learning causal representations using continuous-time neural networks, specifically over their discrete-time counterparts. We evaluate our method in the context of visual-control learning of drones over a series of complex tasks, ranging from short- and long-term navigation, to chasing static and dynamic objects through photorealistic environments. Our results demonstrate that causal continuous-time deep models can perform robust navigation tasks, where advanced recurrent models fail. These models learn complex causal control representations directly from raw visual inputs and scale to solve a variety of tasks using imitation learning.

Probabilistic numerics casts numerical tasks, such the numerical solution of differential equations, as inference problems to be solved. One approach is to model the unknown quantity of interest as a random variable, and to constrain this variable using data generated during the course of a traditional numerical method. However, data may be nonlinearly related to the quantity of interest, rendering the proper conditioning of random variables difficult and limiting the range of numerical tasks that can be addressed. Instead, this paper proposes to construct probabilistic numerical methods based only on the final output from a traditional method. A convergent sequence of approximations to the quantity of interest constitute a dataset, from which the limiting quantity of interest can be extrapolated, in a probabilistic analogue of Richardson's deferred approach to the limit. This black box approach (1) massively expands the range of tasks to which probabilistic numerics can be applied, (2) inherits the features and performance of state-of-the-art numerical methods, and (3) enables provably higher orders of convergence to be achieved. Applications are presented for nonlinear ordinary and partial differential equations, as well as for eigenvalue problems-a setting for which no probabilistic numerical methods have yet been developed.

Kernel selection plays a central role in determining the performance of Gaussian Process (GP) models, as the chosen kernel determines both the inductive biases and prior support of functions under the GP prior. This work addresses the challenge of constructing custom kernel functions for high-dimensional GP regression models. Drawing inspiration from recent progress in deep learning, we introduce a novel approach named KITT: Kernel Identification Through Transformers. KITT exploits a transformer-based architecture to generate kernel recommendations in under 0.1 seconds, which is several orders of magnitude faster than conventional kernel search algorithms. We train our model using synthetic data generated from priors over a vocabulary of known kernels. By exploiting the nature of the self-attention mechanism, KITT is able to process datasets with inputs of arbitrary dimension. We demonstrate that kernels chosen by KITT yield strong performance over a diverse collection of regression benchmarks.

A graph generative model defines a distribution over graphs. One type of generative model is constructed by autoregressive neural networks, which sequentially add nodes and edges to generate a graph. However, the likelihood of a graph under the autoregressive model is intractable, as there are numerous sequences leading to the given graph; this makes maximum likelihood estimation challenging. Instead, in this work we derive the exact joint probability over the graph and the node ordering of the sequential process. From the joint, we approximately marginalize out the node orderings and compute a lower bound on the log-likelihood using variational inference. We train graph generative models by maximizing this bound, without using the ad-hoc node orderings of previous methods. Our experiments show that the log-likelihood bound is significantly tighter than the bound of previous schemes. Moreover, the models fitted with the proposed algorithm can generate high-quality graphs that match the structures of target graphs not seen during training. We have made our code publicly available at \hyperref[https://github.com/tufts-ml/graph-generation-vi]{https://github.com/tufts-ml/graph-generation-vi}.