This paper addresses the problem of computing dense correspondence between 3D shapes in the form of point clouds, which is a challenging and fundamental problem in computer vision and digital geometry processing. Conventional approaches often solve the problem in a supervised manner, requiring massive annotated data, which is difficult and/or expensive to obtain. Motivated by the intuition that one can transform two aligned point clouds to each other more easily and meaningfully than a misaligned pair, we propose CorrNet3D -- the first unsupervised and end-to-end deep learning-based framework -- to drive the learning of dense correspondence by means of deformation-like reconstruction to overcome the need for annotated data. Specifically, CorrNet3D consists of a deep feature embedding module and two novel modules called correspondence indicator and symmetric deformation. Feeding a pair of raw point clouds, our model first learns the pointwise features and passes them into the indicator to generate a learnable correspondence matrix used to permute the input pair. The symmetric deformer, with an additional regularized loss, transforms the two permuted point clouds to each other to drive the unsupervised learning of the correspondence. The extensive experiments on both synthetic and real-world datasets of rigid and non-rigid 3D shapes show our CorrNet3D outperforms state-of-the-art methods to a large extent, including those taking meshes as input. CorrNet3D is a flexible framework in that it can be easily adapted to supervised learning if annotated data are available.

Machine learning based systems are reaching society at large and in many aspects of everyday life. This phenomenon has been accompanied by concerns about the ethical issues that may arise from the adoption of these technologies. ML fairness is a recently established area of machine learning that studies how to ensure that biases in the data and model inaccuracies do not lead to models that treat individuals unfavorably on the basis of characteristics such as e.g. race, gender, disabilities, and sexual or political orientation. In this manuscript, we discuss some of the limitations present in the current reasoning about fairness and in methods that deal with it, and describe some work done by the authors to address them. More specifically, we show how causal Bayesian networks can play an important role to reason about and deal with fairness, especially in complex unfairness scenarios. We describe how optimal transport theory can be used to develop methods that impose constraints on the full shapes of distributions corresponding to different sensitive attributes, overcoming the limitation of most approaches that approximate fairness desiderata by imposing constraints on the lower order moments or other functions of those distributions. We present a unified framework that encompasses methods that can deal with different settings and fairness criteria, and that enjoys strong theoretical guarantees. We introduce an approach to learn fair representations that can generalize to unseen tasks. Finally, we describe a technique that accounts for legal restrictions about the use of sensitive attributes.

We present Language-mediated, Object-centric Representation Learning (LORL), a paradigm for learning disentangled, object-centric scene representations from vision and language. LORL builds upon recent advances in unsupervised object segmentation, notably MONet and Slot Attention. While these algorithms learn an object-centric representation just by reconstructing the input image, LORL enables them to further learn to associate the learned representations to concepts, i.e., words for object categories, properties, and spatial relationships, from language input. These object-centric concepts derived from language facilitate the learning of object-centric representations. LORL can be integrated with various unsupervised segmentation algorithms that are language-agnostic. Experiments show that the integration of LORL consistently improves the object segmentation performance of MONet and Slot Attention on two datasets via the help of language. We also show that concepts learned by LORL, in conjunction with segmentation algorithms such as MONet, aid downstream tasks such as referring expression comprehension.

Conditional inference provides a rigorous approach to counter bias when data from automated model selections is reused for inference. We develop in this paper a statistically consistent Bayesian framework to assess uncertainties within linear models that are informed by grouped sparsities in covariates. Finding wide applications when genes, proteins, genetic variants, neuroimaging measurements are grouped respectively by their biological pathways, molecular functions, regulatory regions, cognitive roles, these models are selected through a useful class of group-sparse learning algorithms. An adjustment factor to account precisely for the selection of promising groups, deployed with a generalized version of Laplace-type approximations is the centerpiece of our new methods. Accommodating well known group-sparse models such as those selected by the Group LASSO, the overlapping Group LASSO, the sparse Group LASSO etc., we illustrate the efficacy of our methodology in extensive experiments and on data from a human neuroimaging application.

Markov Chain Monte Carlo (MCMC) is a class of algorithms to sample complex and high-dimensional probability distributions. The Metropolis-Hastings (MH) algorithm, the workhorse of MCMC, provides a simple recipe to construct reversible Markov kernels. Reversibility is a tractable property which implies a less tractable but essential property here, invariance. Reversibility is however not necessarily desirable when considering performance. This has prompted recent interest in designing kernels breaking this property. At the same time, an active stream of research has focused on the design of novel versions of the MH kernel, some nonreversible, relying on the use of complex invertible deterministic transforms. While standard implementations of the MH kernel are well understood, aforementioned developments have not received the same systematic treatment to ensure their validity. This paper fills the gap by developing general tools to ensure that a class of nonreversible Markov kernels, possibly relying on complex transforms, has the desired invariance property and lead to convergent algorithms. This leads to a set of simple and practically verifiable conditions.

In this paper, we propose a new global analysis framework for a class of low-rank matrix recovery problems on the Riemannian manifold. We analyze the global behavior for the Riemannian optimization with random initialization. We use the Riemannian gradient descent algorithm to minimize a least squares loss function, and study the asymptotic behavior as well as the exact convergence rate. We reveal a previously unknown geometric property of the low-rank matrix manifold, which is the existence of spurious critical points for the simple least squares function on the manifold. We show that under some assumptions, the Riemannian gradient descent starting from a random initialization with high probability avoids these spurious critical points and only converges to the ground truth in nearly linear convergence rate, i.e. $\mathcal{O}(\text{log}(\frac{1}{\epsilon})+ \text{log}(n))$ iterations to reach an $\epsilon$-accurate solution. We use two applications as examples for our global analysis. The first one is a rank-1 matrix recovery problem. The second one is the Gaussian phase retrieval problem. The second example only satisfies the weak isometry property, but has behavior similar to that of the first one except for an extra saddle set. Our convergence guarantee is nearly optimal and almost dimension-free, which fully explains the numerical observations. The global analysis can be potentially extended to other data problems with random measurement structures and empirical least squares loss functions.

Selective forgetting or removing information from deep neural networks (DNNs) is essential for continual learning and is challenging in controlling the DNNs. Such forgetting is crucial also in a practical sense since the deployed DNNs may be trained on the data with outliers, poisoned by attackers, or with leaked/sensitive information. In this paper, we formulate selective forgetting for classification tasks at a finer level than the samples' level. We specify the finer level based on four datasets distinguished by two conditions: whether they contain information to be forgotten and whether they are available for the forgetting procedure. Additionally, we reveal the need for such formulation with the datasets by showing concrete and practical situations. Moreover, we introduce the forgetting procedure as an optimization problem on three criteria; the forgetting, the correction, and the remembering term. Experimental results show that the proposed methods can make the model forget to use specific information for classification. Notably, in specific cases, our methods improved the model's accuracy on the datasets, which contains information to be forgotten but is unavailable in the forgetting procedure. Such data are unexpectedly found and misclassified in actual situations.

Gaussian processes (GPs) are a popular model for spatially referenced data and allow descriptive statements, predictions at new locations, and simulation of new fields. Often a few parameters are sufficient to parameterize the covariance function, and maximum likelihood (ML) methods can be used to estimate these parameters from data. ML methods, however, are computationally demanding. For example, in the case of local likelihood estimation, even fitting covariance models on modest size windows can overwhelm typical computational resources for data analysis. This limitation motivates the idea of using neural network (NN) methods to approximate ML estimates. We train NNs to take moderate size spatial fields or variograms as input and return the range and noise-to-signal covariance parameters. Once trained, the NNs provide estimates with a similar accuracy compared to ML estimation and at a speedup by a factor of 100 or more. Although we focus on a specific covariance estimation problem motivated by a climate science application, this work can be easily extended to other, more complex, spatial problems and provides a proof-of-concept for this use of machine learning in computational statistics.

Nowadays it is inevitable to use intelligent systems to improve the performance and optimization of different components of devices or factories. Furthermore, it's so essential to have appropriate predictions to make better decisions in businesses, medical studies, and engineering studies, etc. One of the newest and most widely used of these methods is a field called'Data Science' that all of the scientists, engineers, and factories need to learn and use them in their careers. This article briefly introduced data science and reviewed its methods, especially it's usages in mechanical engineering and challenges and ways of developing data science in mechanical engineering. In the introduction, different definitions of data science and its background in technology reviewed. In the following, data science methodology which is the process that a data scientist needs to do in its works been discussed. Further, some researches in mechanical engineering area that used data science methods in their studies, are reviewed. Eventually, it has been discussed according to the subjects that have been reviewed in the article, why it is necessary to use data science in mechanical engineering researches and projects.

We present an approach for agents to learn representations of a global map from sensor data, to aid their exploration in new environments. To achieve this, we embed procedures mimicking that of traditional Simultaneous Localization and Mapping (SLAM) into the soft attention based addressing of external memory architectures, in which the external memory acts as an internal representation of the environment. This structure encourages the evolution of SLAM-like behaviors inside a completely differentiable deep neural network. We show that this approach can help reinforcement learning agents to successfully explore new environments where long-term memory is essential. We validate our approach in both challenging grid-world environments and preliminary Gazebo experiments. A video of our experiments can be found at: https://goo.gl/G2Vu5y.