Declutter and Resample: Towards parameter free denoising

In many data analysis applications the following scenario is commonplace: we are given a point set that is supposed to sample a hidden ground truth $K$ in a metric space, but it got corrupted with noise so that some of the data points lie far away from $K$ creating outliers also termed as {\em ambient noise}. One of the main goals of denoising algorithms is to eliminate such noise so that the curated data lie within a bounded Hausdorff distance of $K$. Popular denoising approaches such as deconvolution and thresholding often require the user to set several parameters and/or to choose an appropriate noise model while guaranteeing only asymptotic convergence. Our goal is to lighten this burden as much as possible while ensuring theoretical guarantees in all cases. Specifically, first, we propose a simple denoising algorithm that requires only a single parameter but provides a theoretical guarantee on the quality of the output on general input points. We argue that this single parameter cannot be avoided. We next present a simple algorithm that avoids even this parameter by paying for it with a slight strengthening of the sampling condition on the input points which is not unrealistic. We also provide some preliminary empirical evidence that our algorithms are effective in practice

Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age

Simultaneous Localization and Mapping (SLAM)consists in the concurrent construction of a model of the environment (the map), and the estimation of the state of the robot moving within it. The SLAM community has made astonishing progress over the last 30 years, enabling large-scale real-world applications, and witnessing a steady transition of this technology to industry. We survey the current state of SLAM. We start by presenting what is now the de-facto standard formulation for SLAM. We then review related work, covering a broad set of topics including robustness and scalability in long-term mapping, metric and semantic representations for mapping, theoretical performance guarantees, active SLAM and exploration, and other new frontiers. This paper simultaneously serves as a position paper and tutorial to those who are users of SLAM. By looking at the published research with a critical eye, we delineate open challenges and new research issues, that still deserve careful scientific investigation. The paper also contains the authors' take on two questions that often animate discussions during robotics conferences: Do robots need SLAM? and Is SLAM solved

The Manifold of Neural Responses Informs Physiological Circuits in the Visual System

The rapid development of multi-electrode and imaging techniques is leading to a data explosion in neuroscience, opening the possibility of truly understanding the organization and functionality of our visual systems. Furthermore, the need for more natural visual stimuli greatly increases the complexity of the data. Together, these create a challenge for machine learning. Our goal in this thesis is to develop one such technique. The central pillar of our contribution is designing a manifold of neurons, and providing an algorithmic approach to inferring it. This manifold is functional, in the sense that nearby neurons on the manifold respond similarly (in time) to similar aspects of the stimulus ensemble. By organizing the neurons, our manifold differs from other, standard manifolds as they are used in visual neuroscience which instead organize the stimuli. Our contributions to the machine learning component of the thesis are twofold. First, we develop a tensor representation of the data, adopting a multilinear view of potential circuitry. Tensor factorization then provides an intermediate representation between the neural data and the manifold. We found that the rank of the neural factor matrix can be used to select an appropriate number of tensor factors. Second, to apply manifold learning techniques, a similarity kernel on the data must be defined. Like many others, we employ a Gaussian kernel, but refine it based on a proposed graph sparsification technique—this makes the resulting manifolds less sensitive to the choice of bandwidth parameter. We apply this method to neuroscience data recorded from retina and primary visual cortex in the mouse. For the algorithm to work, however, the underlying circuitry must be exercised to as full an extent as possible. To this end, we develop an ensemble of flow stimuli, which simulate what the mouse would \u27see\u27 running through a field. Applying the algorithm to the retina reveals that neurons form clusters corresponding to known retinal ganglion cell types. In the cortex, a continuous manifold is found, indicating that, from a functional circuit point of view, there may be a continuum of cortical function types. Interestingly, both manifolds share similar global coordinates, which hint at what the key ingredients to vision might be. Lastly, we turn to perhaps the most widely used model for the cortex: deep convolutional networks. Their feedforward architecture leads to manifolds that are even more clustered than the retina, and not at all like that of the cortex. This suggests, perhaps, that they may not suffice as general models for Artificial Intelligence

Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorial

On top of machine learning models, uncertainty quantification (UQ) functions as an essential layer of safety assurance that could lead to more principled decision making by enabling sound risk assessment and management. The safety and reliability improvement of ML models empowered by UQ has the potential to significantly facilitate the broad adoption of ML solutions in high-stakes decision settings, such as healthcare, manufacturing, and aviation, to name a few. In this tutorial, we aim to provide a holistic lens on emerging UQ methods for ML models with a particular focus on neural networks and the applications of these UQ methods in tackling engineering design as well as prognostics and health management problems. Toward this goal, we start with a comprehensive classification of uncertainty types, sources, and causes pertaining to UQ of ML models. Next, we provide a tutorial-style description of several state-of-the-art UQ methods: Gaussian process regression, Bayesian neural network, neural network ensemble, and deterministic UQ methods focusing on spectral-normalized neural Gaussian process. Established upon the mathematical formulations, we subsequently examine the soundness of these UQ methods quantitatively and qualitatively (by a toy regression example) to examine their strengths and shortcomings from different dimensions. Then, we review quantitative metrics commonly used to assess the quality of predictive uncertainty in classification and regression problems. Afterward, we discuss the increasingly important role of UQ of ML models in solving challenging problems in engineering design and health prognostics. Two case studies with source codes available on GitHub are used to demonstrate these UQ methods and compare their performance in the life prediction of lithium-ion batteries at the early stage and the remaining useful life prediction of turbofan engines

Detection of low dimensionality and data denoising via set estimation techniques

This work is closely related to the theories of set estimation and manifold estimation. Our object of interest is a, possibly lower-dimensional, compact set S ⊂ ℝd. The general aim is to identify (via stochastic procedures) some qualitative or quantitative features of S, of geometric or topological character. The available information is just a random sample of points drawn on S. The term “to identify” means here to achieve a correct answer almost surely (a.s.) when the sample size tends to infinity. More specifically the paper aims at giving some partial answers to the following questions: is S full dimensional? Is S “close to a lower dimensional set” M? If so, can we estimate M or some functionals of M (in particular, the Minkowski content of M)? As an important auxiliary tool in the answers of these questions, a denoising procedure is proposed in order to partially remove the noise in the original data. The theoretical results are complemented with some simulations and graphical illustrations. © 2017, Institute of Mathematical Statistics

Graph enabled cross-domain knowledge transfer

The world has never been more connected, led by the information technology revolution in the past decades that has fundamentally changed the way people interact with each other using social networks. Consequently, enormous human activity data are collected from the business world and machine learning techniques are widely adopted to aid our decision processes. Despite of the success of machine learning in various application scenarios, there are still many questions that need to be well answered, such as optimizing machine learning outcomes when desired knowledge cannot be extracted from the available data. This naturally drives us to ponder if one can leverage some side information to populate the knowledge domain of their interest, such that the problems within that knowledge domain can be better tackled. In this work, such problems are investigated and practical solutions are proposed. To leverage machine learning in any decision-making process, one must convert the given knowledge (for example, natural language, unstructured text) into representation vectors that can be understood and processed by machine learning model in their compatible language and data format. The frequently encountered difficulty is, however, the given knowledge is not rich or reliable enough in the first place. In such cases, one seeks to fuse side information from a separate domain to mitigate the gap between good representation learning and the scarce knowledge in the domain of interest. This approach is named Cross-Domain Knowledge Transfer. It is crucial to study the problem because of the commonality of scarce knowledge in many scenarios, from online healthcare platform analyses to financial market risk quantification, leaving an obstacle in front of us benefiting from automated decision making. From the machine learning perspective, the paradigm of semi-supervised learning takes advantage of large amount of data without ground truth and achieves impressive learning performance improvement. It is adopted in this dissertation for cross-domain knowledge transfer. Furthermore, graph learning techniques are indispensable given that networks commonly exist in real word, such as taxonomy networks and scholarly article citation networks. These networks contain additional useful knowledge and are ought to be incorporated in the learning process, which serve as an important lever in solving the problem of cross-domain knowledge transfer. This dissertation proposes graph-based learning solutions and demonstrates their practical usage via empirical studies on real-world applications. Another line of effort in this work lies in leveraging the rich capacity of neural networks to improve the learning outcomes, as we are in the era of big data. In contrast to many Graph Neural Networks that directly iterate on the graph adjacency to approximate graph convolution filters, this work also proposes an efficient Eigenvalue learning method that directly optimizes the graph convolution in the spectral space. This work articulates the importance of network spectrum and provides detailed analyses on the spectral properties in the proposed EigenLearn method, which well aligns with a series of CNN models that attempt to have meaningful spectral interpretation in designing graph neural networks. The disser-tation also addresses the efficiency, which can be categorized in two folds. First, by adopting approximate solutions it mitigates the complexity concerns for graph related algorithms, which are naturally quadratic in most cases and do not scale to large datasets. Second, it mitigates the storage and computation overhead in deep neural network, such that they can be deployed on many light-weight devices and significantly broaden the applicability. Finally, the dissertation is concluded by future endeavors

Graph Enabled Cross-Domain Knowledge Transfer

To leverage machine learning in any decision-making process, one must convert the given knowledge (for example, natural language, unstructured text) into representation vectors that can be understood and processed by machine learning model in their compatible language and data format. The frequently encountered difficulty is, however, the given knowledge is not rich or reliable enough in the first place. In such cases, one seeks to fuse side information from a separate domain to mitigate the gap between good representation learning and the scarce knowledge in the domain of interest. This approach is named Cross-Domain Knowledge Transfer. It is crucial to study the problem because of the commonality of scarce knowledge in many scenarios, from online healthcare platform analyses to financial market risk quantification, leaving an obstacle in front of us benefiting from automated decision making. From the machine learning perspective, the paradigm of semi-supervised learning takes advantage of large amount of data without ground truth and achieves impressive learning performance improvement. It is adopted in this dissertation for cross-domain knowledge transfer. (to be continued