Random forests are a statistical learning method widely used in many areas of scientific research essentially for its ability to learn complex relationship between input and output variables and also its capacity to handle high-dimensional data. However, data are increasingly complex with repeated measures of omics, images leading to shapes, curves... Random forests method is not specifically tailored for them. In this paper, we introduce Fr\'echet trees and Fr\'echet random forests, which allow to manage data for which input and output variables take values in general metric spaces (which can be unordered). To this end, a new way of splitting the nodes of trees is introduced and the prediction procedures of trees and forests are generalized. Then, random forests out-of-bag error and variable importance score are naturally adapted. Finally, the method is studied in the special case of regression on curve shapes, both within a simulation study and a real dataset from an HIV vaccine trial.

In previous work, theoretical analysis based on the tensor Restricted Isometry Property (t-RIP) established the robust recovery guarantees of a low-tubal-rank tensor. The obtained sufficient conditions depend strongly on the assumption that the linear measurement maps satisfy the t-RIP. In this paper, by exploiting the probabilistic arguments, we prove that such linear measurement maps exist under suitable conditions on the number of measurements in terms of the tubal rank r and the size of third-order tensor n1, n2, n3. And the obtained minimal possible number of linear measurements is nearly optimal compared with the degrees of freedom of a tensor with tubal rank r. Specially, we consider a random sub-Gaussian distribution that includes Gaussian, Bernoulli and all bounded distributions and construct a large class of linear maps that satisfy a t-RIP with high probability. Moreover, the validity of the required number of measurements is verified by numerical experiments.

The advent of deep learning has given rise to neural scene representations - learned mathematical models of a 3D environment. However, many of these representations do not explicitly reason about geometry and thus do not account for the underlying 3D structure of the scene. In contrast, geometric deep learning has explored 3D-structure-aware representations of scene geometry, but requires explicit 3D supervision. We propose Scene Representation Networks (SRNs), a continuous, 3D-structure-aware scene representation that encodes both geometry and appearance. SRNs represent scenes as continuous functions that map world coordinates to a feature representation of local scene properties. By formulating the image formation as a differentiable ray-marching algorithm, SRNs can be trained end-to-end from only 2D observations, without access to depth or geometry. This formulation naturally generalizes across scenes, learning powerful geometry and appearance priors in the process. We demonstrate the potential of SRNs by evaluating them for novel view synthesis, few-shot reconstruction, joint shape and appearance interpolation, and unsupervised discovery of a non-rigid face model.

Neural word representations are at the core of many state-of-the-art natural language processing models. A widely used approach is to pre-train, store and look up word or character embedding matrices. While useful, such representations occupy huge memory making it hard to deploy on-device and often do not generalize to unknown words due to vocabulary pruning. In this paper, we propose a skip-gram based architecture coupled with Locality-Sensitive Hashing (LSH) projections to learn efficient dynamically computable representations. Our model does not need to store lookup tables as representations are computed on-the-fly and require low memory footprint. The representations can be trained in an unsupervised fashion and can be easily transferred to other NLP tasks. For qualitative evaluation, we analyze the nearest neighbors of the word representations and discover semantically similar words even with misspellings. For quantitative evaluation, we plug our transferable projections into a simple LSTM and run it on multiple NLP tasks and show how our transferable projections achieve better performance compared to prior work.

Neural generative models have been become increasingly popular when building conversational agents. They offer flexibility, can be easily adapted to new domains, and require minimal domain engineering. A common criticism of these systems is that they seldom understand or use the available dialog history effectively. In this paper, we take an empirical approach to understanding how these models use the available dialog history by studying the sensitivity of the models to artificially introduced unnatural changes or perturbations to their context at test time. We experiment with 10 different types of perturbations on 4 multi-turn dialog datasets and find that commonly used neural dialog architectures like recurrent and transformer-based seq2seq models are rarely sensitive to most perturbations such as missing or reordering utterances, shuffling words, etc. Also, by open-sourcing our code, we believe that it will serve as a useful diagnostic tool for evaluating dialog systems in the future.

Domain Translation is the problem of finding a meaningful correspondence between two domains. Since in a majority of settings paired supervision is not available, much work focuses on Unsupervised Domain Translation (UDT) where data samples from each domain are unpaired. Following the seminal work of CycleGAN for UDT, many variants and extensions of this model have been proposed. However, there is still little theoretical understanding behind their success. We observe that these methods yield solutions which are approximately minimal w.r.t. a given transportation cost, leading us to reformulate the problem in the Optimal Transport (OT) framework. This viewpoint gives us a new perspective on Unsupervised Domain Translation and allows us to prove the existence and uniqueness of the retrieved mapping, given a large family of transport costs. We then propose a novel framework to efficiently compute optimal mappings in a dynamical setting. We show that it generalizes previous methods and enables a more explicit control over the computed optimal mapping. It also provides smooth interpolations between the two domains. Experiments on toy and real world datasets illustrate the behavior of our method.

This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences and interactions. Our problem formulation accordingly trades off rule set complexity and prediction accuracy. Column generation is used to optimize over an exponentially large space of rules without pre-generating a large subset of candidates or greedily boosting rules one by one. The column generation subproblem is solved using either integer programming or a heuristic optimizing the same objective. In experiments involving logistic and linear regression, the proposed methods obtain better accuracy-complexity trade-offs than existing rule ensemble algorithms. At one end of the trade-off, the methods are competitive with less interpretable benchmark models.

Rapid growth in delivery and freight transportation is increasing in urban areas; as a result the use of delivery trucks and light commercial vehicles is evolving. Major cities can use traffic counting as a tool to monitor the presence of delivery vehicles in order to implement intelligent city planning measures. Classical methods for counting vehicles use mechanical, electromagnetic or pneumatic sensors, but these devices are costly, difficult to implement and only detect the presence of vehicles without giving information about their category, model or trajectory. This paper proposes a Deep Learning tool for classifying vehicles in a given image while considering different categories of logistic vehicles, namely: light-duty, medium-duty and heavy-duty vehicles. The proposed approach yields two main contributions: first we developed an architecture to create an annotated and balanced database of logistic vehicles, reducing manual annotation efforts. Second, we built a classifier that accurately classifies the logistic vehicles passing through a given road. The results of this work are: first, a database of 72 000 images for 4 vehicles classes; and second two retrained convolutional neural networks (InceptionV3 and MobileNetV2) capable of classifying vehicles with accuracies over 90%.

Autonomous terrestrial vehicles must be capable of perceiving traffic lights and recognizing their current states to share the streets with human drivers. Most of the time, human drivers can easily identify the relevant traffic lights. To deal with this issue, a common solution for autonomous cars is to integrate recognition with prior maps. However, additional solution is required for the detection and recognition of the traffic light. Deep learning techniques have showed great performance and power of generalization including traffic related problems. Motivated by the advances in deep learning, some recent works leveraged some state-of-the-art deep detectors to locate (and further recognize) traffic lights from 2D camera images. However, none of them combine the power of the deep learning-based detectors with prior maps to recognize the state of the relevant traffic lights. Based on that, this work proposes to integrate the power of deep learning-based detection with the prior maps used by our car platform IARA (acronym for Intelligent Autonomous Robotic Automobile) to recognize the relevant traffic lights of predefined routes. The process is divided in two phases: an offline phase for map construction and traffic lights annotation; and an online phase for traffic light recognition and identification of the relevant ones. The proposed system was evaluated on five test cases (routes) in the city of Vit\'oria, each case being composed of a video sequence and a prior map with the relevant traffic lights for the route. Results showed that the proposed technique is able to correctly identify the relevant traffic light along the trajectory.

We propose and investigate new complementary methodologies for estimating predictive variance networks in regression neural networks. We derive a locally aware mini-batching scheme that result in sparse robust gradients, and show how to make unbiased weight updates to a variance network. Further, we formulate a heuristic for robustly fitting both the mean and variance networks post hoc. Finally, we take inspiration from posterior Gaussian processes and propose a network architecture with similar extrapolation properties to Gaussian processes. The proposed methodologies are complementary, and improve upon baseline methods individually. Experimentally, we investigate the impact on predictive uncertainty on multiple datasets and tasks ranging from regression, active learning and generative modeling. Experiments consistently show significant improvements in predictive uncertainty estimation over state-of-the-art methods across tasks and datasets.