Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are ubiquitous in statistics, machine learning and computer vision, however, this perception has not yet received a theoretical justification. To fill this gap, we prove that computing the Wasserstein distance between a discrete probability measure supported on two points and the Lebesgue measure on the standard hypercube is already #P-hard. This insight prompts us to seek approximate solutions for semi-discrete optimal transport problems. We thus perturb the underlying transportation cost with an additive disturbance governed by an ambiguous probability distribution, and we introduce a distributionally robust dual optimal transport problem whose objective function is smoothed with the most adverse disturbance distributions from within a given ambiguity set. We further show that smoothing the dual objective function is equivalent to regularizing the primal objective function, and we identify several ambiguity sets that give rise to several known and new regularization schemes. As a byproduct, we discover an intimate relation between semi-discrete optimal transport problems and discrete choice models traditionally studied in psychology and economics. To solve the regularized optimal transport problems efficiently, we use a stochastic gradient descent algorithm with imprecise stochastic gradient oracles. A new convergence analysis reveals that this algorithm improves the best known convergence guarantee for semi-discrete optimal transport problems with entropic regularizers.

Federated learning is an appealing framework for analyzing sensitive data from distributed health data networks due to its protection of data privacy. Under this framework, data partners at local sites collaboratively build an analytical model under the orchestration of a coordinating site, while keeping the data decentralized. However, existing federated learning methods mainly assume data across sites are homogeneous samples of the global population, hence failing to properly account for the extra variability across sites in estimation and inference. Drawing on a multi-hospital electronic health records network, we develop an efficient and interpretable tree-based ensemble of personalized treatment effect estimators to join results across hospital sites, while actively modeling for the heterogeneity in data sources through site partitioning. The efficiency of our method is demonstrated by a study of causal effects of oxygen saturation on hospital mortality and backed up by comprehensive numerical results.

This paper proposes a method for solving multivariate regression and classification problems using piecewise linear predictors over a polyhedral partition of the feature space. The resulting algorithm that we call PARC (Piecewise Affine Regression and Classification) alternates between (i) solving ridge regression problems for numeric targets, softmax regression problems for categorical targets, and either softmax regression or cluster centroid computation for piecewise linear separation, and (ii) assigning the training points to different clusters on the basis of a criterion that balances prediction accuracy and piecewise-linear separability. We prove that PARC is a block-coordinate descent algorithm that optimizes a suitably constructed objective function, and that it converges in a finite number of steps to a local minimum of that function. The accuracy of the algorithm is extensively tested numerically on synthetic and real-world datasets, showing that the approach provides an extension of linear regression/classification that is particularly useful when the obtained predictor is used as part of an optimization model. A Python implementation of the algorithm described in this paper is available at http://cse.lab.imtlucca.it/~bemporad/parc .

We present a framework for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy performances and reduced model fitting times, when compared with standard Markov chain Monte Carlo methods. The message passing and factor graph fragment approach to variational Bayes we describe facilitates streamlined implementation of approximate inference algorithms and forms the basis to software development. Such approach allows for supple inclusion of numerous response distributions and penalizations into the inverse problem model. Albeit our analysis is circumscribed to one- and two-dimensional response variables, we lay down an infrastructure where streamlining algorithmic steps based on nullifying weak interactions between variables are extendible to inverse problems in higher dimensions. Image processing applications motivated by biomedical and archaeological problems are included as illustrations.

We consider the problem of estimating a stochastic linear time-invariant (LTI) dynamical system from a single trajectory via streaming algorithms. The problem is equivalent to estimating the parameters of vector auto-regressive (VAR) models encountered in time series analysis (Hamilton (2020)). A recent sequence of papers (Faradonbeh et al., 2018; Simchowitz et al., 2018; Sarkar and Rakhlin, 2019) show that ordinary least squares (OLS) regression can be used to provide optimal finite time estimator for the problem. However, such techniques apply for offline setting where the optimal solution of OLS is available apriori. But, in many problems of interest as encountered in reinforcement learning (RL), it is important to estimate the parameters on the go using gradient oracle. This task is challenging since standard methods like SGD might not perform well when using stochastic gradients from correlated data points (Gy\"orfi and Walk, 1996; Nagaraj et al., 2020). In this work, we propose a novel algorithm, SGD with Reverse Experience Replay (SGD-RER), that is inspired by the experience replay (ER) technique popular in the RL literature (Lin, 1992). SGD-RER divides data into small buffers and runs SGD backwards on the data stored in the individual buffers. We show that this algorithm exactly deconstructs the dependency structure and obtains information theoretically optimal guarantees for both parameter error and prediction error for standard problem settings. Thus, we provide the first - to the best of our knowledge - optimal SGD-style algorithm for the classical problem of linear system identification aka VAR model estimation. Our work demonstrates that knowledge of dependency structure can aid us in designing algorithms which can deconstruct the dependencies between samples optimally in an online fashion.

Cross-lingual word embeddings (CLWE) have been proven useful in many crosslingual tasks. However, most existing approaches to learn CLWE including the ones with contextual embeddings are sense agnostic. In this work, we propose a novel framework to align contextual embeddings at the sense level by leveraging cross-lingual signal from bilingual dictionaries only. We operationalize our framework by first proposing a novel sense-aware cross entropy loss to model word senses explicitly. The monolingual ELMo and BERT models pretrained with our sense-aware cross entropy loss demonstrate significant performance improvement for word sense disambiguation tasks. Compared with the best baseline results, our cross-lingual models achieve 0.52%, 2.09% and 1.29% average performance improvements on zero-shot cross-lingual NER, sentiment classification and XNLI tasks, respectively. Cross-lingual word embeddings (CLWE) provide a shared representation space for knowledge transfer between languages, yielding state-of-the-art performance in many cross-lingual natural language processing (NLP) tasks.

Visual Place Recognition (VPR) is often characterized as being able to recognize the same place despite significant changes in appearance and viewpoint. VPR is a key component of Spatial Artificial Intelligence, enabling robotic platforms and intelligent augmentation platforms such as augmented reality devices to perceive and understand the physical world. In this paper, we observe that there are three "drivers" that impose requirements on spatially intelligent agents and thus VPR systems: 1) the particular agent including its sensors and computational resources, 2) the operating environment of this agent, and 3) the specific task that the artificial agent carries out. In this paper, we characterize and survey key works in the VPR area considering those drivers, including their place representation and place matching choices. We also provide a new definition of VPR based on the visual overlap -- akin to spatial view cells in the brain -- that enables us to find similarities and differences to other research areas in the robotics and computer vision fields. We identify numerous open challenges and suggest areas that require more in-depth attention in future works.

The recent success of reinforcement learning's (RL) in solving complex tasks is most often attributed to its capacity to explore and exploit an environment where it has been trained. Sample efficiency is usually not an issue since cheap simulators are available to sample data on-policy. On the other hand, task oriented dialogues are usually learnt from offline data collected using human demonstrations. Collecting diverse demonstrations and annotating them is expensive. Unfortunately, use of RL methods trained on off-policy data are prone to issues of bias and generalization, which are further exacerbated by stochasticity in human response and non-markovian belief state of a dialogue management system. To this end, we propose a batch RL framework for task oriented dialogue policy learning: causal aware safe policy improvement (CASPI). This method gives guarantees on dialogue policy's performance and also learns to shape rewards according to intentions behind human responses, rather than just mimicking demonstration data; this couple with batch-RL helps overall with sample efficiency of the framework. We demonstrate the effectiveness of this framework on a dialogue-context-to-text Generation and end-to-end dialogue task of the Multiwoz2.0 dataset. The proposed method outperforms the current state of the art on these metrics, in both case. In the end-to-end case, our method trained only on 10\% of the data was able to out perform current state in three out of four evaluation metrics.

Quantum machine learning (QML) can complement the growing trend of using learned models for a myriad of classification tasks, from image recognition to natural speech processing. A quantum advantage arises due to the intractability of quantum operations on a classical computer. Many datasets used in machine learning are crowd sourced or contain some private information. To the best of our knowledge, no current QML models are equipped with privacy-preserving features, which raises concerns as it is paramount that models do not expose sensitive information. Thus, privacy-preserving algorithms need to be implemented with QML. One solution is to make the machine learning algorithm differentially private, meaning the effect of a single data point on the training dataset is minimized. Differentially private machine learning models have been investigated, but differential privacy has yet to be studied in the context of QML. In this study, we develop a hybrid quantum-classical model that is trained to preserve privacy using differentially private optimization algorithm. This marks the first proof-of-principle demonstration of privacy-preserving QML. The experiments demonstrate that differentially private QML can protect user-sensitive information without diminishing model accuracy. Although the quantum model is simulated and tested on a classical computer, it demonstrates potential to be efficiently implemented on near-term quantum devices (noisy intermediate-scale quantum [NISQ]). The approach's success is illustrated via the classification of spatially classed two-dimensional datasets and a binary MNIST classification. This implementation of privacy-preserving QML will ensure confidentiality and accurate learning on NISQ technology.

Dysarthria is a condition which hampers the ability of an individual to control the muscles that play a major role in speech delivery. The loss of fine control over muscles that assist the movement of lips, vocal chords, tongue and diaphragm results in abnormal speech delivery. One can assess the severity level of dysarthria by analyzing the intelligibility of speech spoken by an individual. Continuous intelligibility assessment helps speech language pathologists not only study the impact of medication but also allows them to plan personalized therapy. It helps the clinicians immensely if the intelligibility assessment system is reliable, automatic, simple for (a) patients to undergo and (b) clinicians to interpret. Lack of availability of dysarthric data has resulted in development of speaker dependent automatic intelligibility assessment systems which requires patients to speak a large number of utterances. In this paper, we propose (a) a cost minimization procedure to select an optimal (small) number of utterances that need to be spoken by the dysarthric patient, (b) four different speaker independent intelligibility assessment systems which require the patient to speak a small number of words, and (c) the assessment score is close to the perceptual score that the Speech Language Pathologist (SLP) can relate to. The need for small number of utterances to be spoken by the patient and the score being relatable to the SLP benefits both the dysarthric patient and the clinician from usability perspective.