Accurately monitoring road traffic state and speed is crucial for various applications, including travel time prediction, traffic control, and traffic safety. However, the lack of sensors often results in incomplete traffic state data, making it challenging to obtain reliable information for decision-making. This paper proposes a novel method for imputing traffic state data using Gaussian processes (GP) to address this issue. We propose a kernel rotation re-parametrization scheme that transforms a standard isotropic GP kernel into an anisotropic kernel, which can better model the propagation of traffic waves in traffic flow data. This method can be applied to impute traffic state data from fixed sensors or probe vehicles. Moreover, the rotated GP method provides statistical uncertainty quantification for the imputed traffic state, making it more reliable. We also extend our approach to a multi-output GP, which allows for simultaneously estimating the traffic state for multiple lanes. We evaluate our method using real-world traffic data from the Next Generation simulation (NGSIM) and HighD programs. Considering current and future mixed traffic of connected vehicles (CVs) and human-driven vehicles (HVs), we experiment with the traffic state estimation scheme from 5% to 50% available trajectories, mimicking different CV penetration rates in a mixed traffic environment. Results show that our method outperforms state-of-the-art methods in terms of estimation accuracy, efficiency, and robustness.

In this section, we empirically evaluate the proposed algorithm VIPeR against several state-of-the-art baselines, including (a) PEVI (Jin et al., 2021), which explicitly constructs lower confidence bound (LCB) for pessimism in a linear model (thus, we rename this algorithm as LinLCB for convenience in our experiments); (b) NeuraLCB (Nguyen-Tang et al., 2022a) which explicitly constructs an LCB using neural network gradients; (c) NeuraLCB (Diag), which is NeuraLCB with a diagonal approximation for estimating the confidence set as suggested in NeuraLCB (Nguyen-Tang et al., 2022a); (d) Lin-VIPeR which is VIPeR realized to the linear function approximation instead of neural network function approximation; (e) NeuralGreedy (LinGreedy, respectively) which uses neural networks (linear models, respectively) to fit the offline data and act greedily with respect to the estimated state-action value functions without any pessimism. Note that when the parametric class, F, in Algorithm 1 is that of neural networks, we refer to VIPeR as Neural-VIPeR. We do not utilize data splitting in the experiments. We provide further algorithmic details of the baselines in Section H. We evaluate all algorithms in two problem settings: (1) the underlying MDP is a linear MDP whose reward functions and transition kernels are linear in some known feature map (Jin et al., 2020), and (2) the underlying MDP is non-linear with horizon length H = 1 (i.e., non-linear contextual bandits) (Zhou et al., 2020), where the reward function is either synthetic or constructed from MNIST

Offline reinforcement learning (RL) addresses the problem of learning a performant policy from a fixed batch of data collected by following some behavior policy. Model-based approaches are particularly appealing in the offline setting since they can extract more learning signals from the logged dataset by learning a model of the environment. However, the performance of existing model-based approaches falls short of model-free counterparts, due to the compounding of estimation errors in the learned model. Driven by this observation, we argue that it is critical for a model-based method to understand when to trust the model and when to rely on model-free estimates, and how to act conservatively w.r.t. both. To this end, we derive an elegant and simple methodology called conservative Bayesian model-based value expansion for offline policy optimization (CBOP), that trades off model-free and model-based estimates during the policy evaluation step according to their epistemic uncertainties, and facilitates conservatism by taking a lower bound on the Bayesian posterior value estimate. On the standard D4RL continuous control tasks, we find that our method significantly outperforms previous model-based approaches: e.g., MOPO by $116.4$%, MOReL by $23.2$% and COMBO by $23.7$%. Further, CBOP achieves state-of-the-art performance on $11$ out of $18$ benchmark datasets while doing on par on the remaining datasets.

In this work, we provide a deterministic alternative to the stochastic variational training of generative autoencoders. We refer to these new generative autoencoders as AutoEncoders within Flows (AEF), since the encoder and decoder are defined as affine layers of an overall invertible architecture. This results in a deterministic encoding of the data, as opposed to the stochastic encoding of VAEs. The paper introduces two related families of AEFs. The first family relies on a partition of the ambient space and is trained by exact maximum-likelihood. The second family exploits a deterministic expansion of the ambient space and is trained by maximizing the log-probability in this extended space. This latter case leaves complete freedom in the choice of encoder, decoder and prior architectures, making it a drop-in replacement for the training of existing VAEs and VAE-style models. We show that these AEFs can have strikingly higher performance than architecturally identical VAEs in terms of log-likelihood and sample quality, especially for low dimensional latent spaces. Importantly, we show that AEF samples are substantially sharper than VAE samples.

Recently, Model Predictive Contouring Control (MPCC) has arisen as the state-of-the-art approach for model-based agile flight. MPCC benefits from great flexibility in trading-off between progress maximization and path following at runtime without relying on globally optimized trajectories. However, finding the optimal set of tuning parameters for MPCC is challenging because (i) the full quadrotor dynamics are non-linear, (ii) the cost function is highly non-convex, and (iii) of the high dimensionality of the hyperparameter space. This paper leverages a probabilistic Policy Search method - Weighted Maximum Likelihood (WML)- to automatically learn the optimal objective for MPCC. WML is sample-efficient due to its closed-form solution for updating the learning parameters. Additionally, the data efficiency provided by the use of a model-based approach allows us to directly train in a high-fidelity simulator, which in turn makes our approach able to transfer zero-shot to the real world. We validate our approach in the real world, where we show that our method outperforms both the previous manually tuned controller and the state-of-the-art auto-tuning baseline reaching speeds of 75 km/h.

Self-training is a simple yet effective method within semi-supervised learning. The idea is to iteratively enhance training data by adding pseudo-labeled data. Its generalization performance heavily depends on the selection of these pseudo-labeled data (PLS). In this paper, we aim at rendering PLS more robust towards the involved modeling assumptions. To this end, we propose to select pseudo-labeled data that maximize a multi-objective utility function. The latter is constructed to account for different sources of uncertainty, three of which we discuss in more detail: model selection, accumulation of errors and covariate shift. In the absence of second-order information on such uncertainties, we furthermore consider the generic approach of the generalized Bayesian alpha-cut updating rule for credal sets. As a practical proof of concept, we spotlight the application of three of our robust extensions on simulated and real-world data. Results suggest that in particular robustness w.r.t. model choice can lead to substantial accuracy gains.

Barlow (1985) hypothesized that the co-occurrence of two events $A$ and $B$ is "suspicious" if $P(A,B) \gg P(A) P(B)$. We first review classical measures of association for $2 \times 2$ contingency tables, including Yule's $Y$ (Yule, 1912), which depends only on the odds ratio $\lambda$, and is independent of the marginal probabilities of the table. We then discuss the mutual information (MI) and pointwise mutual information (PMI), which depend on the ratio $P(A,B)/P(A)P(B)$, as measures of association. We show that, once the effect of the marginals is removed, MI and PMI behave similarly to $Y$ as functions of $\lambda$. The pointwise mutual information is used extensively in some research communities for flagging suspicious coincidences, but it is important to bear in mind the sensitivity of the PMI to the marginals, with increased scores for sparser events.

Unsupervised pretraining, which learns a useful representation using a large amount of unlabeled data to facilitate the learning of downstream tasks, is a critical component of modern large-scale machine learning systems. Despite its tremendous empirical success, the rigorous theoretical understanding of why unsupervised pretraining generally helps remains rather limited -- most existing results are restricted to particular methods or approaches for unsupervised pretraining with specialized structural assumptions. This paper studies a generic framework, where the unsupervised representation learning task is specified by an abstract class of latent variable models $\Phi$ and the downstream task is specified by a class of prediction functions $\Psi$. We consider a natural approach of using Maximum Likelihood Estimation (MLE) for unsupervised pretraining and Empirical Risk Minimization (ERM) for learning downstream tasks. We prove that, under a mild ''informative'' condition, our algorithm achieves an excess risk of $\tilde{\mathcal{O}}(\sqrt{\mathcal{C}_\Phi/m} + \sqrt{\mathcal{C}_\Psi/n})$ for downstream tasks, where $\mathcal{C}_\Phi, \mathcal{C}_\Psi$ are complexity measures of function classes $\Phi, \Psi$, and $m, n$ are the number of unlabeled and labeled data respectively. Comparing to the baseline of $\tilde{\mathcal{O}}(\sqrt{\mathcal{C}_{\Phi \circ \Psi}/n})$ achieved by performing supervised learning using only the labeled data, our result rigorously shows the benefit of unsupervised pretraining when $m \gg n$ and $\mathcal{C}_{\Phi\circ \Psi} > \mathcal{C}_\Psi$. This paper further shows that our generic framework covers a wide range of approaches for unsupervised pretraining, including factor models, Gaussian mixture models, and contrastive learning.

I propose a novel approach for nonlinear Logistic regression using a two-layer neural network (NN) model structure with hierarchical priors on the network weights. I present a hybrid of expectation propagation called Variational Expectation Propagation approach (VEP) for approximate integration over the posterior distribution of the weights, the hierarchical scale parameters of the priors and zeta. Using a factorized posterior approximation I derive a computationally efficient algorithm, whose complexity scales similarly to an ensemble of independent sparse logistic models. The approach can be extended beyond standard activation functions and NN model structures to form flexible nonlinear binary predictors from multiple sparse linear models. I consider a hierarchical Bayesian model with logistic regression likelihood and a Gaussian prior distribution over the parameters called weights and hyperparameters. I work in the perspective of E step and M step for computing the approximating posterior and updating the parameters using the computed posterior respectively.

This paper presents an efficient solution to 3D-LiDAR-based Monte Carlo localization (MCL). MCL robustly works if particles are exactly sampled around the ground truth. An inertial navigation system (INS) can be used for accurate sampling, but many particles are still needed to be used for solving the 3D localization problem even if INS is available. In particular, huge number of particles are necessary if INS is not available and it makes infeasible to perform 3D MCL in terms of the computational cost. Scan matching (SM), that is optimization-based localization, efficiently works even though INS is not available because SM can ignore movement constraints of a robot and/or device in its optimization process. However, SM sometimes determines an infeasible estimate against movement. We consider that MCL and SM have complemental advantages and disadvantages and propose a fusion method of MCL and SM. Because SM is considered as optimization of a measurement model in terms of the probabilistic modeling, we perform measurement model optimization as SM. The optimization result is then used to approximate the measurement model distribution and the approximated distribution is used to sample particles. The sampled particles are fused with MCL via importance sampling. As a result, the advantages of MCL and SM can be simultaneously utilized while mitigating their disadvantages. Experiments are conducted on the KITTI dataset and other two open datasets. Results show that the presented method can be run on a single CPU thread and accurately perform localization even if INS is not available.