Müller et al. [2021], Nguyen et al. [2022] builds a GP model for both the function value and the

Machine learning (ML) algorithms can solve many prediction tasks with greater accuracy than classical methods.

We study a general framework of distributional computational graphs: computational graphs whose inputs are probability distributions rather than point values. We analyze the discretization error that arises when these graphs are evaluated using finite approximations of continuous probability distributions. Such an approximation might be the result of representing a continuous real-valued distribution using a discrete representation or from constructing an empirical distribution from samples (or might be the output of another distributional computational graph). We establish non-asymptotic error bounds in terms of the Wasserstein-1 distance, without imposing structural assumptions on the computational graph.

Source code is provided at https://github.com/jdchang1/milo.

Source code is provided at https://github.com/jdchang1/milo.

Motion Transfer is a technique that synthesizes videos by transferring motion dynamics from a driving video to a source image. In this work we propose a deep learning-based framework to enable real-time video motion transfer which is critical for enabling bandwidth-efficient applications such as video conferencing, remote health monitoring, virtual reality interaction, and vision-based anomaly detection. This is done using keypoints which serve as semantically meaningful, compact representations of motion across time. To enable bandwidth savings during video transmission we perform forecasting of keypoints using two generative time series models VRNN and GRU-NF. The predicted keypoints are transformed into realistic video frames using an optical flow-based module paired with a generator network, thereby enabling efficient, low-frame-rate video transmission. Based on the application this allows the framework to either generate a deterministic future sequence or sample a diverse set of plausible futures. Experimental results demonstrate that VRNN achieves the best point-forecast fidelity (lowest MAE) in applications requiring stable and accurate multi-step forecasting and is particularly competitive in higher-uncertainty, multi-modal settings. This is achieved by introducing recurrently conditioned stochastic latent variables that carry past contexts to capture uncertainty and temporal variation. On the other hand the GRU-NF model enables richer diversity of generated videos while maintaining high visual quality. This is realized by learning an invertible, exact-likelihood mapping between the keypoints and their latent representations which supports rich and controllable sampling of diverse yet coherent keypoint sequences. Our work lays the foundation for next-generation AI systems that require real-time, bandwidth-efficient, and semantically controllable video generation.

Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high estimation variance, while large ensembles reduce this variance at the cost of substantial computational overhead and diminished interpretability. In this paper, we propose Decision Tree Embedding (DTE), a fast and effective method that leverages the leaf partitions of a trained classification tree to construct an interpretable feature representation. By using the sample means within each leaf region as anchor points, DTE maps inputs into an embedding space defined by the tree's partition structure, effectively circumventing the high variance inherent in decision-tree splitting rules. We further introduce an ensemble extension based on additional bootstrap trees, and pair the resulting embedding with linear discriminant analysis for classification. We establish several population-level theoretical properties of DTE, including its preservation of conditional density under mild conditions and a characterization of the resulting classification error. Empirical studies on synthetic and real datasets demonstrate that DTE strikes a strong balance between accuracy and computational efficiency, outperforming or matching random forest and shallow neural networks while requiring only a fraction of their training time in most cases. Overall, the proposed DTE method can be viewed either as a scalable decision tree classifier that improves upon standard split rules, or as a neural network model whose weights are learned from tree-derived anchor points, achieving an intriguing integration of both paradigms.

We liberate Equilibrium Propagation (EP) from the limit of infinitesimal perturbations by establishing a finite-nudge foundation for local credit assignment. By modeling network states as Gibbs-Boltzmann distributions rather than deterministic points, we prove that the gradient of the difference in Helmholtz free energy between a nudged and free phase is exactly the difference in expected local energy derivatives. This validates the classic Contrastive Hebbian Learning update as an exact gradient estimator for arbitrary finite nudging, requiring neither infinitesimal approximations nor convexity. Furthermore, we derive a generalized EP algorithm based on the path integral of loss-energy covariances, enabling learning with strong error signals that standard infinitesimal approximations cannot support.

Every day we share our personal information through digital systems which are constantly exposed to threats. For this reason, security-oriented disciplines of signal processing have received increasing attention in the last decades: multimedia forensics, digital watermarking, biometrics, network monitoring, steganography and steganalysis are just a few examples. Even though each of these fields has its own peculiarities, they all have to deal with a common problem: the presence of one or more adversaries aiming at making the system fail. Adversarial Signal Processing lays the basis of a general theory that takes into account the impact that the presence of an adversary has on the design of effective signal processing tools. By focusing on the application side of Adversarial Signal Processing, namely adversarial information fusion in distributed sensor networks, and adopting a game-theoretic approach, this thesis contributes to the above mission by addressing four issues. First, we address decision fusion in distributed sensor networks by developing a novel soft isolation defense scheme that protect the network from adversaries, specifically, Byzantines. Second, we develop an optimum decision fusion strategy in the presence of Byzantines. In the next step, we propose a technique to reduce the complexity of the optimum fusion by relying on a novel near-optimum message passing algorithm based on factor graphs. Finally, we introduce a defense mechanism to protect decentralized networks running consensus algorithm against data falsification attacks.