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Imitation learning has achieved great success in many sequential decision-making tasks, in which a neural agent is learned by imitating collected human demonstrations. However, existing algorithms typically require a large number of high-quality demonstrations that are difficult and expensive to collect. Usually, a trade-off needs to be made between demonstration quality and quantity in practice. Targeting this problem, in this work we consider the imitation of sub-optimal demonstrations, with both a small clean demonstration set and a large noisy set. Some pioneering works have been proposed, but they suffer from many limitations, e.g., assuming a demonstration to be of the same optimality throughout time steps and failing to provide any interpretation w.r.t knowledge learned from the noisy set. Addressing these problems, we propose {\method} by evaluating and imitating at the sub-demonstration level, encoding action primitives of varying quality into different skills. Concretely, {\method} consists of a high-level controller to discover skills and a skill-conditioned module to capture action-taking policies, and is trained following a two-phase pipeline by first discovering skills with all demonstrations and then adapting the controller to only the clean set. A mutual-information-based regularization and a dynamic sub-demonstration optimality estimator are designed to promote disentanglement in the skill space. Extensive experiments are conducted over two gym environments and a real-world healthcare dataset to demonstrate the superiority of {\method} in learning from sub-optimal demonstrations and its improved interpretability by examining learned skills.

The causal dose response curve is commonly selected as the statistical parameter of interest in studies where the goal is to understand the effect of a continuous exposure on an outcome.Most of the available methodology for statistical inference on the dose-response function in the continuous exposure setting requires strong parametric assumptions on the probability distribution. Such parametric assumptions are typically untenable in practice and lead to invalid inference. It is often preferable to instead use nonparametric methods for inference, which only make mild assumptions about the data-generating mechanism. We propose a nonparametric test of the null hypothesis that the dose-response function is equal to a constant function. We argue that when the null hypothesis holds, the dose-response function has zero variance. Thus, one can test the null hypothesis by assessing whether there is sufficient evidence to claim that the variance is positive. We construct a novel estimator for the variance of the dose-response function, for which we can fully characterize the null limiting distribution and thus perform well-calibrated tests of the null hypothesis. We also present an approach for constructing simultaneous confidence bands for the dose-response function by inverting our proposed hypothesis test. We assess the validity of our proposal in a simulation study. In a data example, we study, in a population of patients who have initiated treatment for HIV, how the distance required to travel to an HIV clinic affects retention in care.

We study the problem of model selection in causal inference, specifically for the case of conditional average treatment effect (CATE) estimation under binary treatments. Unlike model selection in machine learning, there is no perfect analogue of cross-validation as we do not observe the counterfactual potential outcome for any data point. Towards this, there have been a variety of proxy metrics proposed in the literature, that depend on auxiliary nuisance models estimated from the observed data (propensity score model, outcome regression model). However, the effectiveness of these metrics has only been studied on synthetic datasets as we can access the counterfactual data for them. We conduct an extensive empirical analysis to judge the performance of these metrics introduced in the literature, and novel ones introduced in this work, where we utilize the latest advances in generative modeling to incorporate multiple realistic datasets. Our analysis suggests novel model selection strategies based on careful hyperparameter tuning of CATE estimators and causal ensembling.

It is often of interest to assess whether a function-valued statistical parameter, such as a density function or a mean regression function, is equal to any function in a class of candidate null parameters. This can be framed as a statistical inference problem where the target estimand is a scalar measure of dissimilarity between the true function-valued parameter and the closest function among all candidate null values. These estimands are typically defined to be zero when the null holds and positive otherwise. While there is well-established theory and methodology for performing efficient inference when one assumes a parametric model for the function-valued parameter, methods for inference in the nonparametric setting are limited. When the null holds, and the target estimand resides at the boundary of the parameter space, existing nonparametric estimators either achieve a non-standard limiting distribution or a sub-optimal convergence rate, making inference challenging. In this work, we propose a strategy for constructing nonparametric estimators with improved asymptotic performance. Notably, our estimators converge at the parametric rate at the boundary of the parameter space and also achieve a tractable null limiting distribution. As illustrations, we discuss how this framework can be applied to perform inference in nonparametric regression problems, and also to perform nonparametric assessment of stochastic dependence.

Semi-parametric Nearest Neighbor Language Models ($k$NN-LMs) have produced impressive gains over purely parametric LMs, by leveraging large-scale neighborhood retrieval over external memory datastores. However, there has been little investigation into adapting such models for new domains. This work attempts to fill that gap and suggests the following approaches for adapting $k$NN-LMs -- 1) adapting the underlying LM (using Adapters), 2) expanding neighborhood retrieval over an additional adaptation datastore, and 3) adapting the weights (scores) of retrieved neighbors using a learned Rescorer module. We study each adaptation strategy separately, as well as the combined performance improvement through ablation experiments and an extensive set of evaluations run over seven adaptation domains. Our combined adaptation approach consistently outperforms purely parametric adaptation and zero-shot ($k$NN-LM) baselines that construct datastores from the adaptation data. On average, we see perplexity improvements of 17.1% and 16% for these respective baselines, across domains.

Market traders often engage in the frequent transaction of volatile assets to optimize their total return. In this study, we introduce a novel investment strategy model, anchored on the 'lazy factor.' Our approach bifurcates into a Price Portfolio Forecasting Model and a Mean-Variance Model with Transaction Costs, utilizing probability weights as the coefficients of laziness factors. The Price Portfolio Forecasting Model, leveraging the EXPMA Mean Method, plots the long-term price trend line and forecasts future price movements, incorporating the tangent slope and rate of change. For short-term investments, we apply the ARIMA Model to predict ensuing prices. The Mean-Variance Model with Transaction Costs employs the Monte Carlo Method to formulate the feasible region. To strike an optimal balance between risk and return, equal probability weights are incorporated as coefficients of the laziness factor. To assess the efficacy of this combined strategy, we executed extensive experiments on a specified dataset. Our findings underscore the model's adaptability and generalizability, indicating its potential to transform investment strategies.

Hybrid dynamical systems, i.e. systems that have both continuous and discrete states, are ubiquitous in engineering, but are difficult to work with due to their discontinuous transitions. For example, a robot leg is able to exert very little control effort while it is in the air compared to when it is on the ground. When the leg hits the ground, the penetrating velocity instantaneously collapses to zero. These instantaneous changes in dynamics and discontinuities (or jumps) in state make standard smooth tools for planning, estimation, control, and learning difficult for hybrid systems. One of the key tools for accounting for these jumps is called the saltation matrix. The saltation matrix is the sensitivity update when a hybrid jump occurs and has been used in a variety of fields including robotics, power circuits, and computational neuroscience. This paper presents an intuitive derivation of the saltation matrix and discusses what it captures, where it has been used in the past, how it is used for linear and quadratic forms, how it is computed for rigid body systems with unilateral constraints, and some of the structural properties of the saltation matrix in these cases.

This paper introduces an efficient and generic framework for finite-element simulations under an implicit time integration scheme. Being compatible with generic constitutive models, a fast matrix assembly method exploits the fact that system matrices are created in a deterministic way as long as the mesh topology remains constant. Using the sparsity pattern of the assembled system brings about significant optimizations on the assembly stage. As a result, developed techniques of GPU-based parallelization can be directly applied with the assembled system. Moreover, an asynchronous Cholesky precondition scheme is used to improve the convergence of the system solver. On this basis, a GPU-based Cholesky preconditioner is developed, significantly reducing the data transfer between the CPU/GPU during the solving stage. We evaluate the performance of our method with different mesh elements and hyperelastic models and compare it with typical approaches on the CPU and the GPU.

Data transformations are essential for broad applicability of parametric regression models. However, for Bayesian analysis, joint inference of the transformation and model parameters typically involves restrictive parametric transformations or nonparametric representations that are computationally inefficient and cumbersome for implementation and theoretical analysis, which limits their usability in practice. This paper introduces a simple, general, and efficient strategy for joint posterior inference of an unknown transformation and all regression model parameters. The proposed approach directly targets the posterior distribution of the transformation by linking it with the marginal distributions of the independent and dependent variables, and then deploys a Bayesian nonparametric model via the Bayesian bootstrap. Crucially, this approach delivers (1) joint posterior consistency under general conditions, including multiple model misspecifications, and (2) efficient Monte Carlo (not Markov chain Monte Carlo) inference for the transformation and all parameters for important special cases. These tools apply across a variety of data domains, including real-valued, integer-valued, compactly-supported, and positive data. Simulation studies and an empirical application demonstrate the effectiveness and efficiency of this strategy for semiparametric Bayesian analysis with linear models, quantile regression, and Gaussian processes.

Unsupervised domain adaptation has recently emerged as an effective paradigm for generalizing deep neural networks to new target domains. However, there is still enormous potential to be tapped to reach the fully supervised performance. In this paper, we present a novel active learning strategy to assist knowledge transfer in the target domain, dubbed active domain adaptation. We start from an observation that energy-based models exhibit free energy biases when training (source) and test (target) data come from different distributions. Inspired by this inherent mechanism, we empirically reveal that a simple yet efficient energy-based sampling strategy sheds light on selecting the most valuable target samples than existing approaches requiring particular architectures or computation of the distances. Our algorithm, Energy-based Active Domain Adaptation (EADA), queries groups of targe data that incorporate both domain characteristic and instance uncertainty into every selection round. Meanwhile, by aligning the free energy of target data compact around the source domain via a regularization term, domain gap can be implicitly diminished. Through extensive experiments, we show that EADA surpasses state-of-the-art methods on well-known challenging benchmarks with substantial improvements, making it a useful option in the open world. Code is available at //github.com/BIT-DA/EADA.