Observation-specific explanations through scattered data approximation

This work introduces the definition of observation-specific explanations to assign a score to each data point proportional to its importance in the definition of the prediction process. Such explanations involve the identification of the most influential observations for the black-box model of interest. The proposed method involves estimating these explanations by constructing a surrogate model through scattered data approximation utilizing the orthogonal matching pursuit algorithm. The proposed approach is validated on both simulated and real-world datasets.

Fast Empirical Scenarios

We seek to extract a small number of representative scenarios from large and high-dimensional panel data that are consistent with sample moments. Among two novel algorithms, the first identifies scenarios that have not been observed before, and comes with a scenario-based representation of covariance matrices. The second proposal picks important data points from states of the world that have already realized, and are consistent with higher-order sample moment information. Both algorithms are efficient to compute, and lend themselves to consistent scenario-based modeling and high-dimensional numerical integration. Extensive numerical benchmarking studies and an application in portfolio optimization favor the proposed algorithms.

Samplet basis pursuit

We consider kernel-based learning in samplet coordinates with l1-regularization. The application of an l1-regularization term enforces sparsity of the coefficients with respect to the samplet basis. Therefore, we call this approach samplet basis pursuit. Samplets are wavelet-type signed measures, which are tailored to scattered data. They provide similar properties as wavelets in terms of localization, multiresolution analysis, and data compression. The class of signals that can sparsely be represented in a samplet basis is considerably larger than the class of signals which exhibit a sparse representation in the single-scale basis. In particular, every signal that can be represented by the superposition of only a few features of the canonical feature map is also sparse in samplet coordinates. We propose the efficient solution of the problem under consideration by combining soft-shrinkage with the semi-smooth Newton method and compare the approach to the fast iterative shrinkage thresholding algorithm. We present numerical benchmarks as well as applications to surface reconstruction from noisy data and to the reconstruction of temperature data using a dictionary of multiple kernels.

Anisotropic multiresolution analyses for deepfake detection

Generative Adversarial Networks (GANs) have paved the path towards entirely new media generation capabilities at the forefront of image, video, and audio synthesis. However, they can also be misused and abused to fabricate elaborate lies, capable of stirring up the public debate. The threat posed by GANs has sparked the need to discern between genuine content and fabricated one. Previous studies have tackled this task by using classical machine learning techniques, such as k-nearest neighbours and eigenfaces, which unfortunately did not prove very effective. Subsequent methods have focused on leveraging on frequency decompositions, i.e., discrete cosine transform, wavelets, and wavelet packets, to preprocess the input features for classifiers. However, existing approaches only rely on isotropic transformations. We argue that, since GANs primarily utilize isotropic convolutions to generate their output, they leave clear traces, their fingerprint, in the coefficient distribution on sub-bands extracted by anisotropic transformations. We employ the fully separable wavelet transform and multiwavelets to obtain the anisotropic features to feed to standard CNN classifiers. Lastly, we find the fully separable transform capable of improving the state-of-the-art.

Adaptive joint distribution learning

We develop a new framework for embedding (joint) probability distributions in tensor product reproducing kernel Hilbert spaces (RKHS). This framework accommodates a low-dimensional, positive, and normalized model of a Radon-Nikodym derivative, estimated from sample sizes of up to several million data points, alleviating the inherent limitations of RKHS modeling. Well-defined normalized and positive conditional distributions are natural by-products to our approach. The embedding is fast to compute and naturally accommodates learning problems ranging from prediction to classification. The theoretical findings are supplemented by favorable numerical results.

Samplets: A new paradigm for data compression

In this article, we introduce the concept of samplets by transferring the construction of Tausch-White wavelets to the realm of data. This way we obtain a multilevel representation of discrete data which directly enables data compression, detection of singularities and adaptivity. Applying samplets to represent kernel matrices, as they arise in kernel based learning or Gaussian process regression, we end up with quasi-sparse matrices. By thresholding small entries, these matrices are compressible to O(N log N) relevant entries, where N is the number of data points. This feature allows for the use of fill-in reducing reorderings to obtain a sparse factorization of the compressed matrices. Besides the comprehensive introduction to samplets and their properties, we present extensive numerical studies to benchmark the approach. Our results demonstrate that samplets mark a considerable step in the direction of making large data sets accessible for analysis.