The problem at the heart of this tutorial consists in modeling the path choice behavior of network users. This problem has extensively been studied in transportation science and econometrics, where it is known as the route choice problem. In this literature, individuals' choice of paths are typically predicted from discrete choice models. The aim of this tutorial is to present this problem from the novel and more general perspective of inverse optimization, in order to describe the modeling approaches proposed in related research areas and thereby motivate the use of so-called recursive models. The latter have the advantage of predicting path choices without generating choice sets. In this paper, we contextualize discrete choice models as a probabilistic approach to an inverse shortest path problem with noisy data, highlighting that recursive discrete choice models in particular originate from viewing the inner shortest path problem as a parametric Markov Decision Process. We also illustrate through simple numerical examples that recursive models overcome issues associated with the path-based discrete choice models commonly found in the transportation literature.

In this work an iterative algorithm based on unsupervised learning is presented, specifically on a Restricted Boltzmann Machine (RBM) to solve a perfect matching problem on a bipartite weighted graph. Iteratively is calculated the weights $w_{ij}$ and the bias parameters $\theta = ( a_i, b_j) $ that maximize the energy function and assignment element $i$ to element $j$. An application of real problem is presented to show the potentiality of this algorithm.

Bayesian optimization (BO) is a powerful approach for seeking the global optimum of expensive black-box functions and has proven successful for fine tuning hyper-parameters of machine learning models. The Bayesian optimization routine involves learning a response surface and maximizing a score to select the most valuable inputs to be queried at the next iteration. These key steps are subject to the curse of dimensionality so that Bayesian optimization does not scale beyond 10--20 parameters. In this work, we address this issue and propose a high-dimensional BO method that learns a nonlinear low-dimensional manifold of the input space. We achieve this with a multi-layer neural network embedded in the covariance function of a Gaussian process. This approach applies unsupervised dimensionality reduction as a byproduct of a supervised regression solution. This also allows exploiting data efficiency of Gaussian process models in a Bayesian framework. We also introduce a nonlinear mapping from the manifold to the high-dimensional space based on multi-output Gaussian processes and jointly train it end-to-end via marginal likelihood maximization. We show this intrinsically low-dimensional optimization outperforms recent baselines in high-dimensional BO literature on a set of benchmark functions in 60 dimensions.

Real-world autonomous vehicles often operate in a priori unknown environments. Since most of these systems are safety-critical, it is important to ensure they operate safely in the face of environment uncertainty, such as unseen obstacles. Current safety analysis tools enable autonomous systems to reason about safety given full information about the state of the environment a priori. However, these tools do not scale well to scenarios where the environment is being sensed in real time, such as during navigation tasks. In this work, we propose a novel, real-time safety analysis method based on Hamilton-Jacobi reachability that provides strong safety guarantees despite environment uncertainty. Our safety method is planner-agnostic and provides guarantees for a variety of mapping sensors. We demonstrate our approach in simulation and in hardware to provide safety guarantees around a state-of-the-art vision-based, learning-based planner.

Modern intelligent transportation systems provide data that allow real-time demand prediction, which is essential for planning and operations. The main challenge of prediction of Origin-Destination (O-D) flow matrices is that demands cannot be directly measured by traffic sensors; instead, they have to be inferred from aggregate traffic flow data on traffic links. Specifically, spatial correlation, congestion and time dependent factors need to be considered in general transportation networks. In this paper we propose a novel O-D prediction framework based on Fusion Line Graph Convolutional Networks (FL-GCNs). We use FL-GCN to recognize spatial and temporal patterns simultaneously. The underlying road network topology is transformed into a corresponding line graph. This structure provides a general framework for predicting spatial-temporal O-D information from link traffic flows. Data from a New Jersey Turnpike network is used to evaluate the proposed model. The results show that FL-GCN can recognize spatial and temporal patterns. We also compare FL-GCN with Kalman filter; the results show that our model can outperform Kalman filter by 17.87% in predicting the whole O-D pairs.

Sequence modeling is a fundamental real-world problem with a wide range of applications. Recurrent neural networks (RNNs) are currently preferred in sequence prediction tasks due to their ability to model long-term and variable order dependencies. However, RNNs have disadvantages in several applications because of their inability to natively handle uncertainty, and because of the inscrutable internal representations. Probabilistic sequence models like Hidden Markov Models (HMM) have the advantage of more interpretable representations and the ability to handle uncertainty. Although overcomplete HMMs with many more hidden states compared to the observed states can, in theory, model long-term temporal dependencies [23], training HMMs is challenging due to credit diffusion [3]. For this reason, simpler and inflexible n-gram models are preferred to HMMs for tasks like language modeling. Tensor decomposition methods [1] have been suggested for the learning of HMMs in order to overcome the credit diffusion problem, but current methods are not applicable to the overcomplete setting where the full-rank requirements on the transition and emission matrices are not fulfilled. Recently there has been renewed interest in the topic of training overcomplete HMMs for higher-order dependencies with the expectation that sparsity structures could potentially alleviate the credit diffusion problem [23]. In this paper we demonstrate that a particular sparsity structure on the emission matrix can help HMMs learn higher-order temporal structure using the standard Expectation-Maximization algorithms [26] (Baum-Welch) and its online variants.

Model-free Reinforcement Learning (RL) algorithms such as Q-learning [Watkins, Dayan 92] have been widely used in practice and can achieve human level performance in applications such as video games [Mnih et al. 15]. Recently, equipped with the idea of optimism in the face of uncertainty, Q-learning algorithms [Jin, Allen-Zhu, Bubeck, Jordan 18] can be proven to be sample efficient for discrete tabular Markov Decision Processes (MDPs) which have finite number of states and actions. In this work, we present an efficient model-free Q-learning based algorithm in MDPs with a natural metric on the state-action space--hence extending efficient model-free Q-learning algorithms to continuous state-action space. Compared to previous model-based RL algorithms for metric spaces [Kakade, Kearns, Langford 03], our algorithm does not require access to a black-box planning oracle.

Brain tumor segmentation from Magnetic Resonance Images (MRIs) is an important task to measure tumor responses to treatments. However, automatic segmentation is very challenging. This paper presents an automatic brain tumor segmentation method based on a Normalized Gaussian Bayesian classification and a new 3D Fluid Vector Flow (FVF) algorithm. In our method, a Normalized Gaussian Mixture Model (NGMM) is proposed and used to model the healthy brain tissues. Gaussian Bayesian Classifier is exploited to acquire a Gaussian Bayesian Brain Map (GBBM) from the test brain MR images. GBBM is further processed to initialize the 3D FVF algorithm, which segments the brain tumor. This algorithm has two major contributions. First, we present a NGMM to model healthy brains. Second, we extend our 2D FVF algorithm to 3D space and use it for brain tumor segmentation. The proposed method is validated on a publicly available dataset.

Statistical learning theory has been studied for general function estimation from data since the late 1960's [22]. However, it was only widely adopted in practice after the introduction of the learning algorithms known as Support Vector Machines (SVMs) [23]. Using the so-called kernel trick, which replaces dot products between features and model parameters by evaluations of a kernel function, SVMs can learn nonlinear relations from training patterns by solving a convex optimization problem [16]. An important variant of the SVM is the Least Squares Support Vector Machine (LS-SVM) [20], which is obtained by making all data points supportvectors. LS-SVM avoids the constrained quadratic optimization step of standard SVMs by replacing the training procedure with one that reduces to solving a system of linear equations, which can be performed via ordinary least squares. The first SVM formulation was derived for classification tasks, but it has been readily adapted to tackle regression problems, being usually named Support Vector Regression (SVR) [6]. Similarly, the regression counterpart of LS-SVM is the LS-SVR [20]. 1

We introduce a probabilistic framework for quantifying the semantic similarity between two groups of embeddings. We formulate the task of semantic similarity as a model comparison task in which we contrast a generative model which jointly models two sentences versus one that does not. We illustrate how this framework can be used for the Semantic Textual Similarity tasks using clear assumptions about how the embeddings of words are generated. We apply model comparison that utilises information criteria to address some of the shortcomings of Bayesian model comparison, whilst still penalising model complexity. We achieve competitive results by applying the proposed framework with an appropriate choice of likelihood on the STS datasets.