In human pedagogy, teachers and students can interact adaptively to maximize communication efficiency. The teacher adjusts her teaching method for different students, and the student, after getting familiar with the teacher's instruction mechanism, can infer the teacher's intention to learn faster. Recently, the benefits of integrating this cooperative pedagogy into machine concept learning in discrete spaces have been proved by multiple works. However, how cooperative pedagogy can facilitate machine parameter learning hasn't been thoroughly studied. In this paper, we propose a gradient optimization based teacher-aware learner who can incorporate teacher's cooperative intention into the likelihood function and learn provably faster compared with the naive learning algorithms used in previous machine teaching works. We give theoretical proof that the iterative teacher-aware learning (ITAL) process leads to local and global improvements. We then validate our algorithms with extensive experiments on various tasks including regression, classification, and inverse reinforcement learning using synthetic and real data. We also show the advantage of modeling teacher-awareness when agents are learning from human teachers.

Recently, the information-theoretical framework has been proven to be able to obtain non-vacuous generalization bounds for large models trained by Stochastic Gradient Langevin Dynamics (SGLD) with isotropic noise. In this paper, we optimize the information-theoretical generalization bound by manipulating the noise structure in SGLD. We prove that with constraint to guarantee low empirical risk, the optimal noise covariance is the square root of the expected gradient covariance if both the prior and the posterior are jointly optimized. This validates that the optimal noise is quite close to the empirical gradient covariance. Technically, we develop a new information-theoretical bound that enables such an optimization analysis. We then apply matrix analysis to derive the form of optimal noise covariance. Presented constraint and results are validated by the empirical observations.

The need for algorithms able to solve Reinforcement Learning (RL) problems with few trials has motivated the advent of model-based RL methods. The reported performance of model-based algorithms has dramatically increased within recent years. However, it is not clear how much of the recent progress is due to improved algorithms or due to improved models. While different modeling options are available to choose from when applying a model-based approach, the distinguishing traits and particular strengths of different models are not clear. The main contribution of this work lies precisely in assessing the model influence on the performance of RL algorithms. A set of commonly adopted models is established for the purpose of model comparison. These include Neural Networks (NNs), ensembles of NNs, two different approximations of Bayesian NNs (BNNs), that is, the Concrete Dropout NN and the Anchored Ensembling, and Gaussian Processes (GPs). The model comparison is evaluated on a suite of continuous control benchmarking tasks. Our results reveal that significant differences in model performance do exist. The Concrete Dropout NN reports persistently superior performance. We summarize these differences for the benefit of the modeler and suggest that the model choice is tailored to the standards required by each specific application.

The time-domain simulation is the fundamental tool for power system transient stability analysis. Accurate and reliable simulations rely on accurate dynamic component modeling. In practical power systems, dynamic component modeling has long faced the challenges of model determination and model calibration, especially with the rapid development of renewable generation and power electronics. In this paper, based on the general framework of neural ordinary differential equations (ODEs), a modified neural ODE module and a neural differential-algebraic equations (DAEs) module for power system dynamic component modeling are proposed. The modules adopt an autoencoder to raise the dimension of state variables, model the dynamics of components with artificial neural networks (ANNs), and keep the numerical integration structure. In the neural DAE module, an additional ANN is used to calculate injection currents. The neural models can be easily integrated into time-domain simulations. With datasets consisting of sampled curves of input variables and output variables, the proposed modules can be used to fulfill the tasks of parameter inference, physics-data-integrated modeling, black-box modeling, etc., and can be easily integrated into power system dynamic simulations. Some simple numerical tests are carried out in the IEEE-39 system and prove the validity and potentiality of the proposed modules.

Many of us (myself included) have felt discouraged from using Bayesian statistics for analysis. Supposedly, Bayesian statistics has a bad reputation: it is difficult and heavily dependent on math. Also, because of its relevance to many fields, Data Science included, writers and professionals, want to get a head start by publishing articles on how the formula works. I believe data professionals, academics, existing books, and online courses are responsible for creating the negative stereotype of Bayes' hard work. We can all agree that not everyone is attracted to mathematical formulas.

Box-Cox transformation is commonly used remedy when the normality is not met. This comherensive guide includes estimation techniques and use of Box-Cox transformation in practice. Find out how to apply Box-Cox transformation in R. In this tutorial, we will work on Box-Cox transformation in R. Firstly, we will mention two types of estimation techniques for Box-Cox transformation parameter. These are maximum likelihood estimation (MLE) and estimation via normality tests. Secondly, we will work how to apply Box-Cox transformation in practice.

It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success in adopting a deep network for feature extraction followed by a GP used as function model. Recently,it was suggested that, albeit training with marginal likelihood, the deterministic nature of feature extractor might lead to overfitting while the replacement with a Bayesian network seemed to cure it. Here, we propose the conditional Deep Gaussian Process (DGP) in which the intermediate GPs in hierarchical composition are supported by the hyperdata and the exposed GP remains zero mean. Motivated by the inducing points in sparse GP, the hyperdata also play the role of function supports, but are hyperparameters rather than random variables. We follow our previous moment matching approach to approximate the marginal prior for conditional DGP with a GP carrying an effective kernel. Thus, as in empirical Bayes, the hyperdata are learned by optimizing the approximate marginal likelihood which implicitly depends on the hyperdata via the kernel. We shall show the equivalence with the deep kernel learning in the limit of dense hyperdata in latent space. However, the conditional DGP and the corresponding approximate inference enjoy the benefit of being more Bayesian than deep kernel learning. Preliminary extrapolation results demonstrate expressive power from the depth of hierarchy by exploiting the exact covariance and hyperdata learning, in comparison with GP kernel composition, DGP variational inference and deep kernel learning. We also address the non-Gaussian aspect of our model as well as way of upgrading to a full Bayes inference.

Humans are expert explorers. Understanding the computational cognitive mechanisms that support this efficiency can advance the study of the human mind and enable more efficient exploration algorithms. We hypothesize that humans explore new environments efficiently by inferring the structure of unobserved spaces using spatial information collected from previously explored spaces. This cognitive process can be modeled computationally using program induction in a Hierarchical Bayesian framework that explicitly reasons about uncertainty with strong spatial priors. Using a new behavioral Map Induction Task, we demonstrate that this computational framework explains human exploration behavior better than non-inductive models and outperforms state-of-the-art planning algorithms when applied to a realistic spatial navigation domain.

A few-shot generative model should be able to generate data from a distribution by only observing a limited set of examples. In few-shot learning the model is trained on data from many sets from different distributions sharing some underlying properties such as sets of characters from different alphabets or sets of images of different type objects. We study a latent variables approach that extends the Neural Statistician [8] to a fully hierarchical approach with an attention-based point to set-level aggregation. We extend the previous work to iterative data sampling, likelihood-based model comparison, and adaptation-free out of distribution generalization. Our results show that the hierarchical formulation better captures the intrinsic variability within the sets in the small data regime. With this work we generalize deep latent variable approaches to few-shot learning, taking a step towards large-scale few-shot generation with a formulation that readily can work with current state-of-the-art deep generative models.

Roth (1996) proved that any form of marginal inference with probabilistic graphical models (e.g. Bayesian Networks) will at least be NP-hard. Introduced and extensively investigated in the past decade, the neural probabilistic circuits known as sum-product network (SPN) offers linear time complexity. On another note, research around neural causal models (NCM) recently gained traction, demanding a tighter integration of causality for machine learning. To this end, we present a theoretical investigation of if, when, how and under what cost tractability occurs for different NCM. We prove that SPN-based causal inference is generally tractable, opposed to standard MLP-based NCM. We further introduce a new tractable NCM-class that is efficient in inference and fully expressive in terms of Pearl's Causal Hierarchy. Our comparative empirical illustration on simulations and standard benchmarks validates our theoretical proofs.