2,032 research outputs found
Online Isotonic Regression
We consider the online version of the isotonic regression problem. Given a
set of linearly ordered points (e.g., on the real line), the learner must
predict labels sequentially at adversarially chosen positions and is evaluated
by her total squared loss compared against the best isotonic (non-decreasing)
function in hindsight. We survey several standard online learning algorithms
and show that none of them achieve the optimal regret exponent; in fact, most
of them (including Online Gradient Descent, Follow the Leader and Exponential
Weights) incur linear regret. We then prove that the Exponential Weights
algorithm played over a covering net of isotonic functions has a regret bounded
by and present a matching
lower bound on regret. We provide a computationally efficient version of this
algorithm. We also analyze the noise-free case, in which the revealed labels
are isotonic, and show that the bound can be improved to or even to
(when the labels are revealed in isotonic order). Finally, we extend the
analysis beyond squared loss and give bounds for entropic loss and absolute
loss.Comment: 25 page
Graph Optimization Approach to Range-based Localization
In this paper, we propose a general graph optimization based framework for
localization, which can accommodate different types of measurements with
varying measurement time intervals. Special emphasis will be on range-based
localization. Range and trajectory smoothness constraints are constructed in a
position graph, then the robot trajectory over a sliding window is estimated by
a graph based optimization algorithm. Moreover, convergence analysis of the
algorithm is provided, and the effects of the number of iterations and window
size in the optimization on the localization accuracy are analyzed. Extensive
experiments on quadcopter under a variety of scenarios verify the effectiveness
of the proposed algorithm and demonstrate a much higher localization accuracy
than the existing range-based localization methods, especially in the altitude
direction
Machine Learning Approaches to Human Body Shape Analysis
Soft biometrics, biomedical sciences, and many other fields of study pay particular attention to the study of the geometric description of the human body, and its variations. Although multiple contributions, the interest is particularly high given the non-rigid nature of the human body, capable of assuming different poses, and numerous shapes due to variable body composition. Unfortunately, a well-known costly requirement in data-driven machine learning, and particularly in the human-based analysis, is the availability of data, in the form of geometric information (body measurements) with related vision information (natural images, 3D mesh, etc.). We introduce a computer graphics framework able to generate thousands of synthetic human body meshes, representing a population of individuals with stratified information: gender, Body Fat Percentage (BFP), anthropometric measurements, and pose. This contribution permits an extensive analysis of different bodies in different poses, avoiding the demanding, and expensive acquisition process. We design a virtual environment able to take advantage of the generated bodies, to infer the body surface area (BSA) from a single view. The framework permits to simulate the acquisition process of newly introduced RGB-D devices disentangling different noise components (sensor noise, optical distortion, body part occlusions). Common geometric descriptors in soft biometric, as well as in biomedical sciences, are based on body measurements. Unfortunately, as we prove, these descriptors are not pose invariant, constraining the usability in controlled scenarios. We introduce a differential geometry approach assuming body pose variations as isometric transformations of the body surface, and body composition changes covariant to the body surface area. This setting permits the use of the Laplace-Beltrami operator on the 2D body manifold, describing the body with a compact, efficient, and pose invariant representation. We design a neural network architecture able to infer important body semantics from spectral descriptors, closing the gap between abstract spectral features, and traditional measurement-based indices. Studying the manifold of body shapes, we propose an innovative generative adversarial model able to learn the body shapes. The method permits to generate new bodies with unseen geometries as a walk on the latent space, constituting a significant advantage over traditional generative methods
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