Deep learning algorithms have recently shown to be a successful tool in estimating parameters of statistical models for which simulation is easy, but likelihood computation is challenging. But the success of these approaches depends on simulating parameters that sufficiently reproduce the observed data, and, at present, there is a lack of efficient methods to produce these simulations. We develop new black-box procedures to estimate parameters of statistical models based only on weak parameter structure assumptions. For well-structured likelihoods with frequent occurrences, such as in time series, this is achieved by pre-training a deep neural network on an extensive simulated database that covers a wide range of data sizes. For other types of complex dependencies, an iterative algorithm guides simulations to the correct parameter region in multiple rounds. These approaches can successfully estimate and quantify the uncertainty of parameters from non-Gaussian models with complex spatial and temporal dependencies. The success of our methods is a first step towards a fully flexible automatic black-box estimation framework.
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Over-approximating (OX) program logics, such as separation logic (SL), are used for verifying properties of heap-manipulating programs: all terminating behaviour is characterised, but established results and errors need not be reachable. OX function specifications are thus incompatible with true bug-finding supported by symbolic execution tools such as Pulse and Pulse-X. In contrast, under-approximating (UX) program logics, such as incorrectness separation logic, are used to find true results and bugs: established results and errors are reachable, but there is no mechanism for understanding if all terminating behaviour has been characterised. We introduce exact separation logic (ESL), which provides fully-verified function specifications compatible with both OX verification and UX true bug-funding: all terminating behaviour is characterised, and all established results and errors are reachable. We prove soundness for ESL with mutually recursive functions, demonstrating, for the first time, function compositionality for a UX logic. We show that UX program logics require subtle definitions of internal and external function specifications compared with the familiar definitions of OX logics. We investigate the expressivity of ESL and, for the first time, explore the role of abstraction in UX reasoning by verifying abstract ESL specifications of various data-structure algorithms. In doing so, we highlight the difference between abstraction (hiding information) and over-approximation (losing information). Our findings demonstrate that, expectedly, abstraction cannot be used as freely in UX logics as in OX logics, but also that it should be feasible to use ESL to provide tractable function specifications for self-contained, critical code, which would then be used for both verification and true bug-finding.
Autonomous vehicles are continually increasing their presence on public roads. However, before any new autonomous driving software can be approved, it must first undergo a rigorous assessment of driving quality. These quality evaluations typically focus on estimating the frequency of (undesirable) behavioral events. While rate estimation would be straight-forward with complete data, in the autonomous driving setting this estimation is greatly complicated by the fact that \textit{detecting} these events within large driving logs is a non-trivial task that often involves human reviewers. In this paper we outline a \textit{streaming partial tiered event review} configuration that ensures both high recall and high precision on the events of interest. In addition, the framework allows for valid streaming estimates at any phase of the data collection process, even when labels are incomplete, for which we develop the maximum likelihood estimate and show it is unbiased. Constructing honest and effective confidence intervals (CI) for these rate estimates, particularly for rare safety-critical events, is a novel and challenging statistical problem due to the complexity of the data likelihood. We develop and compare several CI approximations, including a novel Gamma CI method that approximates the exact but intractable distribution with a weighted sum of independent Poisson random variables. There is a clear trade-off between statistical coverage and interval width across the different CI methods, and the extent of this trade-off varies depending on the specific application settings (e.g., rare vs. common events). In particular, we argue that our proposed CI method is the best-suited when estimating the rate of safety-critical events where guaranteed coverage of the true parameter value is a prerequisite to safely launching a new ADS on public roads.
We study estimation of causal effects in staggered rollout designs, i.e. settings where there is staggered treatment adoption and the timing of treatment is as-good-as randomly assigned. We derive the most efficient estimator in a class of estimators that nests several popular generalized difference-in-differences methods. A feasible plug-in version of the efficient estimator is asymptotically unbiased with efficiency (weakly) dominating that of existing approaches. We provide both $t$-based and permutation-test-based methods for inference. In an application to a training program for police officers, confidence intervals for the proposed estimator are as much as eight times shorter than for existing approaches.
We study distributionally robust offline reinforcement learning (robust offline RL), which seeks to find an optimal robust policy purely from an offline dataset that can perform well in perturbed environments. We propose a generic algorithm framework \underline{D}oubly \underline{P}essimistic \underline{M}odel-based \underline{P}olicy \underline{O}ptimization ($\texttt{P}^2\texttt{MPO}$) for robust offline RL, which features a novel combination of a flexible model estimation subroutine and a doubly pessimistic policy optimization step. The \emph{double pessimism} principle is crucial to overcome the distributional shift incurred by i) the mismatch between behavior policy and the family of target policies; and ii) the perturbation of the nominal model. Under certain accuracy assumptions on the model estimation subroutine, we show that $\texttt{P}^2\texttt{MPO}$ is provably efficient with \emph{robust partial coverage data}, which means that the offline dataset has good coverage of the distributions induced by the optimal robust policy and perturbed models around the nominal model. By tailoring specific model estimation subroutines for concrete examples including tabular Robust Markov Decision Process (RMDP), factored RMDP, and RMDP with kernel and neural function approximations, we show that $\texttt{P}^2\texttt{MPO}$ enjoys a $\tilde{\mathcal{O}}(n^{-1/2})$ convergence rate, where $n$ is the number of trajectories in the offline dataset. Notably, these models, except for the tabular case, are first identified and proven tractable by this paper. To the best of our knowledge, we first propose a general learning principle -- double pessimism -- for robust offline RL and show that it is provably efficient in the context of general function approximations.
Range-only (RO) localization involves determining the position of a mobile robot by measuring the distance to specific anchors. RO localization is challenging since the measurements are low-dimensional and a single range sensor does not have enough information to estimate the full pose of the robot. As such, range sensors are typically coupled with other sensing modalities such as wheel encoders or inertial measurement units (IMUs) to estimate the full pose. In this work, we propose a continuous-time Gaussian process (GP)- based trajectory estimation method to estimate the full pose of a robot using only range measurements from multiple range sensors. Results from simulation and real experiments show that our proposed method, using off-the-shelf range sensors, is able to achieve comparable performance and in some cases outperform alternative state-of-the-art sensor-fusion methods that use additional sensing modalities.
In many fields, the acquisition of advanced models depends on large datasets, making data storage and model training expensive. As a solution, dataset distillation can synthesize a small dataset that preserves most information of the original large dataset. The recently proposed dataset distillation method by matching network parameters has been proven effective for several datasets. However, the dimensions of network parameters are typically large. Furthermore, some parameters are difficult to match during the distillation process, degrading distillation performance. Based on this observation, this study proposes a novel dataset distillation method based on parameter pruning that solves the problem. The proposed method can synthesize more robust distilled datasets and improve distillation performance by pruning difficult-to-match parameters during the distillation process. Experimental results on three datasets show that the proposed method outperforms other state-of-the-art dataset distillation methods.
A Two-Stage approach enables researchers to make optimal non-linear predictions via Generalized Ridge Regression using models that contain two or more x-predictor variables and make only realistic minimal assumptions. The optimal regression coefficient estimates that result are either unbiased or most likely to have mininal MSE risk under Normal distribution theory. All necessary calculations and graphical displays are generated using current versions of CRAN R-packages. A numerical example using the "corrected" USArrests data.frame introduces and illustrates this new robust statistical methodology. While applying this strategy to regression models with several hundred observations is straight-forward, the computations required in such cases can be extensive.
Originally introduced as a neural network for ensemble learning, mixture of experts (MoE) has recently become a fundamental building block of highly successful modern deep neural networks for heterogeneous data analysis in several applications, including those in machine learning, statistics, bioinformatics, economics, and medicine. Despite its popularity in practice, a satisfactory level of understanding of the convergence behavior of Gaussian-gated MoE parameter estimation is far from complete. The underlying reason for this challenge is the inclusion of covariates in the Gaussian gating and expert networks, which leads to their intrinsically complex interactions via partial differential equations with respect to their parameters. We address these issues by designing novel Voronoi loss functions to accurately capture heterogeneity in the maximum likelihood estimator (MLE) for resolving parameter estimation in these models. Our results reveal distinct behaviors of the MLE under two settings: the first setting is when all the location parameters in the Gaussian gating are non-zeros while the second setting is when there exists at least one zero-valued location parameter. Notably, these behaviors can be characterized by the solvability of two different systems of polynomial equations. Finally, we conduct a simulation study to verify our theoretical results.
Even when the causal graph underlying our data is unknown, we can use observational data to narrow down the possible values that an average treatment effect (ATE) can take by (1) identifying the graph up to a Markov equivalence class; and (2) estimating that ATE for each graph in the class. While the PC algorithm can identify this class under strong faithfulness assumptions, it can be computationally prohibitive. Fortunately, only the local graph structure around the treatment is required to identify the set of possible ATE values, a fact exploited by local discovery algorithms to improve computational efficiency. In this paper, we introduce Local Discovery using Eager Collider Checks (LDECC), a new local causal discovery algorithm that leverages unshielded colliders to orient the treatment's parents differently from existing methods. We show that there exist graphs where LDECC exponentially outperforms existing local discovery algorithms and vice versa. Moreover, we show that LDECC and existing algorithms rely on different faithfulness assumptions, leveraging this insight to weaken the assumptions for identifying the set of possible ATE values.
Classic machine learning methods are built on the $i.i.d.$ assumption that training and testing data are independent and identically distributed. However, in real scenarios, the $i.i.d.$ assumption can hardly be satisfied, rendering the sharp drop of classic machine learning algorithms' performances under distributional shifts, which indicates the significance of investigating the Out-of-Distribution generalization problem. Out-of-Distribution (OOD) generalization problem addresses the challenging setting where the testing distribution is unknown and different from the training. This paper serves as the first effort to systematically and comprehensively discuss the OOD generalization problem, from the definition, methodology, evaluation to the implications and future directions. Firstly, we provide the formal definition of the OOD generalization problem. Secondly, existing methods are categorized into three parts based on their positions in the whole learning pipeline, namely unsupervised representation learning, supervised model learning and optimization, and typical methods for each category are discussed in detail. We then demonstrate the theoretical connections of different categories, and introduce the commonly used datasets and evaluation metrics. Finally, we summarize the whole literature and raise some future directions for OOD generalization problem. The summary of OOD generalization methods reviewed in this survey can be found at //out-of-distribution-generalization.com.
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