Image Based Rendering Using Algebraic Techniques

This paper presents an image-based rendering system using algebraic relations between different views of an object. The system uses pictures of an object taken from known positions. Given three such images it can generate "virtual'' ones as the object would look from any position near the ones that the two input images were taken from. The extrapolation from the example images can be up to about 60 degrees of rotation. The system is based on the trilinear constraints that bind any three view so fan object. As a side result, we propose two new methods for camera calibration. We developed and used one of them. We implemented the system and tested it on real images of objects and faces. We also show experimentally that even when only two images taken from unknown positions are given, the system can be used to render the object from other view points as long as we have a good estimate of the internal parameters of the camera used and we are able to find good correspondence between the example images. In addition, we present the relation between these algebraic constraints and a factorization method for shape and motion estimation. As a result we propose a method for motion estimation in the special case of orthographic projection

A New Approach to Collaborative Filtering: Operator Estimation with Spectral Regularization

We present a general approach for collaborative filtering (CF) using spectral regularization to learn linear operators from "users" to the "objects" they rate. Recent low-rank type matrix completion approaches to CF are shown to be special cases. However, unlike existing regularization based CF methods, our approach can be used to also incorporate information such as attributes of the users or the objects -- a limitation of existing regularization based CF methods. We then provide novel representer theorems that we use to develop new estimation methods. We provide learning algorithms based on low-rank decompositions, and test them on a standard CF dataset. The experiments indicate the advantages of generalizing the existing regularization based CF methods to incorporate related information about users and objects. Finally, we show that certain multi-task learning methods can be also seen as special cases of our proposed approach

The need for a system view to regulate artificial intelligence/machine learning-based software as medical device

Artificial intelligence (AI) and Machine learning (ML) systems in medicine are poised to significantly improve health care, for example, by offering earlier diagnoses of diseases or recommending optimally individualized treatment plans. However, the emergence of AI/ML in medicine also creates challenges, which regulators must pay attention to. Which medical AI/ML-based products should be reviewed by regulators? What evidence should be required to permit marketing for AI/ML-based software as a medical device (SaMD)? How can we ensure the safety and effectiveness of AI/ML-based SaMD that may change over time as they are applied to new data? The U.S. Food and Drug Administration (FDA), for example, has recently proposed a discussion paper to address some of these issues. But it misses an important point: we argue that regulators like the FDA need to widen their scope from evaluating medical AI/ML-based products to assessing systems. This shift in perspective—from a product view to a system view—is central to maximizing the safety and efficacy of AI/ML in health care, but it also poses significant challenges for agencies like the FDA who are used to regulating products, not systems. We offer several suggestions for regulators to make this challenging but important transition

Sparse Representations of Multiple Signals

We discuss the problem of finding sparse representations of a class of signals. We formalize the problem and prove it is NP-complete both in the case of a single signal and that of multiple ones. Next we develop a simple approximation method to the problem and we show experimental results using artificially generated signals. Furthermore,we use our approximation method to find sparse representations of classes of real signals, specifically of images of pedestrians. We discuss the relation between our formulation of the sparsity problem and the problem of finding representations of objects that are compact and appropriate for detection and classification

Landmines in Eritrea: The Socio-Economic Impact, Prioritisation and Integration on the Basis of Community Visits

The PricewaterhouseCoopers Ulysses leadership program led to this study. It discusses the socio-economic impact of landmines, the benefits of mine action, the prioritisation and integration of mine action within national development priorities. It was carried out so as to understand how landmine contamination has affected the lives of people living in the landmine impacted communities of Eritrea, and focuses purely on an economic cost-benefit analysis

From Regression to Classification in Support Vector Machines

We study the relation between support vector machines (SVMs) for regression (SVMR) and SVM for classification (SVMC). We show that for a given SVMC solution there exists a SVMR solution which is equivalent for a certain choice of the parameters. In particular our result is that for $epsilon$ sufficiently close to one, the optimal hyperplane and threshold for the SVMC problem with regularization parameter C_c are equal to (1-epsilon)^{- 1} times the optimal hyperplane and threshold for SVMR with regularization parameter C_r = (1-epsilon)C_c. A direct consequence of this result is that SVMC can be seen as a special case of SVMR

Manipulation Risks in Explainable AI: The Implications of the Disagreement Problem

Artificial Intelligence (AI) systems are increasingly used in high-stakes domains of our life, increasing the need to explain these decisions and to make sure that they are aligned with how we want the decision to be made. The field of Explainable AI (XAI) has emerged in response. However, it faces a significant challenge known as the disagreement problem, where multiple explanations are possible for the same AI decision or prediction. While the existence of the disagreement problem is acknowledged, the potential implications associated with this problem have not yet been widely studied. First, we provide an overview of the different strategies explanation providers could deploy to adapt the returned explanation to their benefit. We make a distinction between strategies that attack the machine learning model or underlying data to influence the explanations, and strategies that leverage the explanation phase directly. Next, we analyse several objectives and concrete scenarios the providers could have to engage in this behavior, and the potential dangerous consequences this manipulative behavior could have on society. We emphasize that it is crucial to investigate this issue now, before these methods are widely implemented, and propose some mitigation strategies

Dictionary Learning and Tensor Decomposition via the Sum-of-Squares Method

We give a new approach to the dictionary learning (also known as "sparse coding") problem of recovering an unknown $n\times m$ matrix $A$ (for $m \geq n$) from examples of the form $$y = Ax + e,$$ where $x$ is a random vector in $\mathbb R^m$ with at most $\tau m$ nonzero coordinates, and $e$ is a random noise vector in $\mathbb R^n$ with bounded magnitude. For the case $m=O(n)$, our algorithm recovers every column of $A$ within arbitrarily good constant accuracy in time $m^{O(\log m/\log(\tau^{-1}))}$, in particular achieving polynomial time if $\tau = m^{-\delta}$ for any $\delta>0$, and time $m^{O(\log m)}$ if $\tau$ is (a sufficiently small) constant. Prior algorithms with comparable assumptions on the distribution required the vector $x$ to be much sparser---at most $\sqrt{n}$ nonzero coordinates---and there were intrinsic barriers preventing these algorithms from applying for denser $x$. We achieve this by designing an algorithm for noisy tensor decomposition that can recover, under quite general conditions, an approximate rank-one decomposition of a tensor $T$, given access to a tensor $T'$ that is $\tau$-close to $T$ in the spectral norm (when considered as a matrix). To our knowledge, this is the first algorithm for tensor decomposition that works in the constant spectral-norm noise regime, where there is no guarantee that the local optima of $T$ and $T'$ have similar structures. Our algorithm is based on a novel approach to using and analyzing the Sum of Squares semidefinite programming hierarchy (Parrilo 2000, Lasserre 2001), and it can be viewed as an indication of the utility of this very general and powerful tool for unsupervised learning problems