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It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…

Kernel methods on discrete domains have shown great promise for many challenging data types, for instance, biological sequence data and molecular structure data. Scalable kernel methods like Support Vector Machines may offer good predictive…

We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…

Spatial transcriptomics (ST) technologies enable gene expression profiling with spatial resolution, offering unprecedented insights into tissue organization and disease heterogeneity. However, current analysis methods often struggle with…

This thesis focuses on data that has complex spatio-temporal structure and on probabilistic graphical models that learn the structure in an interpretable and scalable manner. We target two research areas of interest: Gaussian graphical…

Many machine learning tasks can benefit from external knowledge. Large knowledge graphs store such knowledge, and embedding methods can be used to distill it into ready-to-use vector representations for downstream applications. For this…

Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. A key issue is how to address the inherent non-linearity of classical deep learning, a problem in the quantum domain due to…

Modern deep learning for asset allocation typically separates forecasting from optimization. We argue this creates a fundamental mismatch where minimizing prediction errors fails to yield robust portfolios. We propose the Signature Informed…

Signed graphs are powerful models for representing complex relations with both positive and negative connections. Recently, Signed Graph Neural Networks (SGNNs) have emerged as potent tools for analyzing such graphs. To our knowledge, no…

Single-cell gene expression measurements encode variability spanning molecular noise, cell-to-cell heterogeneity, and technical artifacts. Mechanistic stochastic models provide powerful approaches to disentangle these sources, yet inferring…

Anomaly detection in multivariate signals is a task of paramount importance in many disciplines (epidemiology, finance, cognitive sciences and neurosciences, oncology, etc.). In this perspective, Topological Data Analysis (TDA) offers a…

Generative methods for graphs need to be sufficiently flexible to model complex dependencies between sets of nodes. At the same time, the generated graphs need to satisfy domain-dependent feasibility conditions, that is, they should not…

Graphs serve as generic tools to encode the underlying relational structure of data. Often this graph is not given, and so the task of inferring it from nodal observations becomes important. Traditional approaches formulate a convex inverse…

Ray tracing has become a standard for accurate radio propagation modeling, but suffers from exponential computational complexity, as the number of candidate paths scales with the number of objects raised to the interaction order. This…

Quantum circuits that generate coherent superpositions of stochastic processes are key to many downstream quantum-accelerated tasks, such as risk analysis, importance sampling, and DNA sequencing. However, traditional methods for designing…

Traditional saliency map methods, popularized in computer vision, highlight individual points (pixels) of the input that contribute the most to the model's output. However, in time series, they offer limited insights, as semantically…

We introduce complex-valued tensor network models for sequence processing motivated by correspondence to probabilistic graphical models, interpretability and resource compression. Inductive bias is introduced to our models via network…

Merging the two cultures of deep and statistical learning provides insights into structured high-dimensional data. Traditional statistical modeling is still a dominant strategy for structured tabular data. Deep learning can be viewed…

Graph neural networks (GNNs) have been predominantly driven by message-passing, where node representations are iteratively updated via local neighborhood aggregation. Despite their success, message-passing suffers from fundamental…

Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. We provide Gaussian process models based on pseudo-likelihood approximation to perform sequence labeling. Gaussian…