Hyperspectral feature spaces are useful for many remote sensing applications ranging from spectral mixture modeling to discrete thematic classification. In such cases, characterization of the feature space dimensionality, geometry and topology can provide guidance for effective model design. The objective of this study is to compare and contrast two approaches for identifying feature space basis vectors via dimensionality reduction. These approaches can be combined to render a joint characterization that reveals spectral properties not apparent using either approach alone. We use a diverse collection of AVIRIS-NG reflectance spectra of the snow-firn-ice continuum to illustrate the utility of joint characterization and identify physical properties inferred from the spectra. Spectral feature spaces combining principal components (PCs) and t-distributed Stochastic Neighbor Embeddings (t-SNEs) provide physically interpretable dimensions representing the global (PC) structure of cryospheric reflectance properties and local (t-SNE) manifold structures revealing clustering not resolved in the global continuum. Joint characterization reveals distinct continua for snow-firn gradients on different parts of the Greenland Ice Sheet and multiple clusters of ice reflectance properties common to both glacier and sea ice in different locations. Clustering revealed in t-SNE feature spaces, and extended to the joint characterization, distinguishes differences in spectral curvature specific to location within the snow accumulation zone, and BRDF effects related to view geometry. The ability of PC+t-SNE joint characterization to produce a physically interpretable spectral feature spaces revealing global topology while preserving local manifold structures suggests that this characterization might be extended to the much higher dimensional hyperspectral feature space of all terrestrial land cover.
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Given a probability distribution $\mathcal{D}$ over the non-negative integers, a $\mathcal{D}$-repeat channel acts on an input symbol by repeating it a number of times distributed as $\mathcal{D}$. For example, the binary deletion channel ($\mathcal{D}=Bernoulli$) and the Poisson repeat channel ($\mathcal{D}=Poisson$) are special cases. We say a $\mathcal{D}$-repeat channel is square-integrable if $\mathcal{D}$ has finite first and second moments. In this paper, we construct explicit codes for all square-integrable $\mathcal{D}$-repeat channels with rate arbitrarily close to the capacity, that are encodable and decodable in linear and quasi-linear time, respectively. We also consider possible extensions to the repeat channel model, and illustrate how our construction can be extended to an even broader class of channels capturing insertions, deletions, and substitutions. Our work offers an alternative, simplified, and more general construction to the recent work of Rubinstein (arXiv:2111.00261), who attains similar results to ours in the cases of the deletion channel and the Poisson repeat channel. It also slightly improves the runtime and decoding failure probability of the polar codes constructions of Tal et al. (ISIT 2019) and of Pfister and Tal (arXiv:2102.02155) for the deletion channel and certain insertion/deletion/substitution channels. Our techniques follow closely the approaches of Guruswami and Li (IEEEToIT 2019) and Con and Shpilka (IEEEToIT 2020); what sets apart our work is that we show that a capacity-achieving code can be assumed to have an "approximate balance" in the frequency of zeros and ones of all sufficiently long substrings of all codewords. This allows us to attain near-capacity-achieving codes in a general setting. We consider this "approximate balance" result to be of independent interest, as it can be cast in much greater generality than repeat channels.
We present a novel attack against the Combined Charging System, one of the most widely used DC rapid charging systems for electric vehicles (EVs). Our attack, Brokenwire, interrupts necessary control communication between the vehicle and charger, causing charging sessions to abort. The attack can be conducted wirelessly from a distance, allowing individual vehicles or entire fleets to be disrupted stealthily and simultaneously. In addition, it can be mounted with off-the-shelf radio hardware and minimal technical knowledge. The exploited behavior is a required part of the HomePlug Green PHY, DIN 70121 & ISO 15118 standards and all known implementations exhibit it. We first study the attack in a controlled testbed and then demonstrate it against seven vehicles and 18 chargers in real deployments. We find the attack to be successful in the real world, at ranges up to 47 m, for a power budget of less than 1 W. We further show that the attack can work between the floors of a building (e.g., multi-story parking), through perimeter fences, and from 'drive-by' attacks. We present a heuristic model to estimate the number of vehicles that can be attacked simultaneously for a given output power. Brokenwire has immediate implications for many of the around 12 million battery EVs on the roads worldwide - and profound effects on the new wave of electrification for vehicle fleets, both for private enterprise and crucial public services. As such, we conducted a disclosure to the industry and discussed a range of mitigation techniques that could be deployed to limit the impact.
The classic Reinforcement Learning (RL) formulation concerns the maximization of a scalar reward function. More recently, convex RL has been introduced to extend the RL formulation to all the objectives that are convex functions of the state distribution induced by a policy. Notably, convex RL covers several relevant applications that do not fall into the scalar formulation, including imitation learning, risk-averse RL, and pure exploration. In classic RL, it is common to optimize an infinite trials objective, which accounts for the state distribution instead of the empirical state visitation frequencies, even though the actual number of trajectories is always finite in practice. This is theoretically sound since the infinite trials and finite trials objectives can be proved to coincide and thus lead to the same optimal policy. In this paper, we show that this hidden assumption does not hold in the convex RL setting. In particular, we show that erroneously optimizing the infinite trials objective in place of the actual finite trials one, as it is usually done, can lead to a significant approximation error. Since the finite trials setting is the default in both simulated and real-world RL, we believe shedding light on this issue will lead to better approaches and methodologies for convex RL, impacting relevant research areas such as imitation learning, risk-averse RL, and pure exploration among others.
Classical two-sample permutation tests for equality of distributions have exact size in finite samples, but they fail to control size for testing equality of parameters that summarize each distribution. This paper proposes permutation tests for equality of parameters that are estimated at root-$n$ or slower rates. Our general framework applies to both parametric and nonparametric models, with two samples or one sample split into two subsamples. Our tests have correct size asymptotically while preserving exact size in finite samples when distributions are equal. They have no loss in local-asymptotic power compared to tests that use asymptotic critical values. We propose confidence sets with correct coverage in large samples that also have exact coverage in finite samples if distributions are equal up to a transformation. We apply our theory to four commonly-used hypothesis tests of nonparametric functions evaluated at a point. Lastly, simulations show good finite sample properties, and two empirical examples illustrate our tests in practice.
In this paper, we consider data acquired by multimodal sensors capturing complementary aspects and features of a measured phenomenon. We focus on a scenario in which the measurements share mutual sources of variability but might also be contaminated by other measurement-specific sources such as interferences or noise. Our approach combines manifold learning, which is a class of nonlinear data-driven dimension reduction methods, with the well-known Riemannian geometry of symmetric and positive-definite (SPD) matrices. Manifold learning typically includes the spectral analysis of a kernel built from the measurements. Here, we take a different approach, utilizing the Riemannian geometry of the kernels. In particular, we study the way the spectrum of the kernels changes along geodesic paths on the manifold of SPD matrices. We show that this change enables us, in a purely unsupervised manner, to derive a compact, yet informative, description of the relations between the measurements, in terms of their underlying components. Based on this result, we present new algorithms for extracting the common latent components and for identifying common and measurement-specific components.
The efficiency of Markov Chain Monte Carlo (MCMC) depends on how the underlying geometry of the problem is taken into account. For distributions with strongly varying curvature, Riemannian metrics help in efficient exploration of the target distribution. Unfortunately, they have significant computational overhead due to e.g. repeated inversion of the metric tensor, and current geometric MCMC methods using the Fisher information matrix to induce the manifold are in practice slow. We propose a new alternative Riemannian metric for MCMC, by embedding the target distribution into a higher-dimensional Euclidean space as a Monge patch and using the induced metric determined by direct geometric reasoning. Our metric only requires first-order gradient information and has fast inverse and determinants, and allows reducing the computational complexity of individual iterations from cubic to quadratic in the problem dimensionality. We demonstrate how Lagrangian Monte Carlo in this metric efficiently explores the target distributions.
Wearable devices such as the ActiGraph are now commonly used in health studies to monitor or track physical activity. This trend aligns well with the growing need to accurately assess the effects of physical activity on health outcomes such as obesity. When accessing the association between these device-based physical activity measures with health outcomes such as body mass index, the device-based data is considered functions, while the outcome is a scalar-valued. The regression model applied in these settings is the scalar-on-function regression (SoFR). Most estimation approaches in SoFR assume that the functional covariates are precisely observed, or the measurement errors are considered random errors. Violation of this assumption can lead to both under-estimation of the model parameters and sub-optimal analysis. The literature on a measurement corrected approach in SoFR is sparse in the non-Bayesian literature and virtually non-existent in the Bayesian literature. This paper considers a fully nonparametric Bayesian measurement error corrected SoFR model that relaxes all the constraining assumptions often made in these models. Our estimation relies on an instrumental variable (IV) to identify the measurement error model. Finally, we introduce an IV quality scalar parameter that is jointly estimated along with all model parameters. Our method is easy to implement, and we demonstrate its finite sample properties through an extensive simulation. Finally, the developed methods are applied to the National Health and Examination Survey to assess the relationship between wearable-device-based measures of physical activity and body mass index among adults living in the United States.
Multiplying matrices is among the most fundamental and compute-intensive operations in machine learning. Consequently, there has been significant work on efficiently approximating matrix multiplies. We introduce a learning-based algorithm for this task that greatly outperforms existing methods. Experiments using hundreds of matrices from diverse domains show that it often runs $100\times$ faster than exact matrix products and $10\times$ faster than current approximate methods. In the common case that one matrix is known ahead of time, our method also has the interesting property that it requires zero multiply-adds. These results suggest that a mixture of hashing, averaging, and byte shuffling$-$the core operations of our method$-$could be a more promising building block for machine learning than the sparsified, factorized, and/or scalar quantized matrix products that have recently been the focus of substantial research and hardware investment.
The area of Data Analytics on graphs promises a paradigm shift as we approach information processing of classes of data, which are typically acquired on irregular but structured domains (social networks, various ad-hoc sensor networks). Yet, despite its long history, current approaches mostly focus on the optimization of graphs themselves, rather than on directly inferring learning strategies, such as detection, estimation, statistical and probabilistic inference, clustering and separation from signals and data acquired on graphs. To fill this void, we first revisit graph topologies from a Data Analytics point of view, and establish a taxonomy of graph networks through a linear algebraic formalism of graph topology (vertices, connections, directivity). This serves as a basis for spectral analysis of graphs, whereby the eigenvalues and eigenvectors of graph Laplacian and adjacency matrices are shown to convey physical meaning related to both graph topology and higher-order graph properties, such as cuts, walks, paths, and neighborhoods. Next, to illustrate estimation strategies performed on graph signals, spectral analysis of graphs is introduced through eigenanalysis of mathematical descriptors of graphs and in a generic way. Finally, a framework for vertex clustering and graph segmentation is established based on graph spectral representation (eigenanalysis) which illustrates the power of graphs in various data association tasks. The supporting examples demonstrate the promise of Graph Data Analytics in modeling structural and functional/semantic inferences. At the same time, Part I serves as a basis for Part II and Part III which deal with theory, methods and applications of processing Data on Graphs and Graph Topology Learning from data.
We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.
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