In recent years, persistent homology, one of the flagship concepts of Topological Data Analysis (TDA), has found its use in many fields such as neuroscience, material science, sensor networks, shape recognition, gene expression data analysis and many more Giunti et al. (2022). The performance of machine learning models such as Graph Neural Networks (GNNs) can be enhanced by augmenting topological information captured by persistent homology (Hofer et al., 2017; Dehmamy et al., 2019; Carrière et al., 2020; Horn et al., 2022). Classical persistent homology, also known as 1-parameter persistence, captures the evolution of topological structures in a simplicial complex K following a filter function f: K R. The evolution of topological structures, in this case, can be completely characterized and compactly represented as persistence diagrams or equivalently barcodes Zomorodian & Carlsson (2004); Edelsbrunner et al. (2002). These persistence diagrams or barcodes can be vectorized Bubenik (2015); Reininghaus et al. (2015); Adams et al. (2017); Hofer et al. (2019); Carrière et al. (2020); Kim et al. (2020) and used in machine learning pipelines. In most applications, the simplicial complex K is given and the choice of the filter function f depends on the application. Choosing an appropriate filter function can be challenging. To avoid this, in Hofer et al. (2020), the authors proposed an end-to-end learning framework to learn the filter function rather than relying on making the right choice. They showed that learning the filter function performs better than the standard choices of filter functions on many graph datasets.

Recent research efforts on adversarial machine learning (ML) have investigated problem-space attacks, focusing on the generation of real evasive objects in domains where, unlike images, there is no clear inverse mapping to the feature space (e.g., software). However, the design, comparison, and real-world implications of problem-space attacks remain underexplored. This article makes three major contributions. Firstly, we propose a general formalization for adversarial ML evasion attacks in the problem-space, which includes the definition of a comprehensive set of constraints on available transformations, preserved semantics, absent artifacts, and plausibility. We shed light on the relationship between feature space and problem space, and we introduce the concept of side-effect features as the by-product of the inverse feature-mapping problem. This enables us to define and prove necessary and sufficient conditions for the existence of problem-space attacks. Secondly, building on our general formalization, we propose a novel problem-space attack on Android malware that overcomes past limitations in terms of semantics and artifacts. We have tested our approach on a dataset with 150K Android apps from 2016 and 2018 which show the practical feasibility of evading a state-of-the-art malware classifier along with its hardened version. Thirdly, we explore the effectiveness of adversarial training as a possible approach to enforce robustness against adversarial samples, evaluating its effectiveness on the considered machine learning models under different scenarios. Our results demonstrate that "adversarial-malware as a service" is a realistic threat, as we automatically generate thousands of realistic and inconspicuous adversarial applications at scale, where on average it takes only a few minutes to generate an adversarial instance.

Recent work has suggested using Monte Carlo methods based on piecewise deterministic Markov processes (PDMPs) to sample from target distributions of interest. PDMPs are non-reversible continuous-time processes endowed with momentum, and hence can mix better than standard reversible MCMC samplers. Furthermore, they can incorporate exact sub-sampling schemes which only require access to a single (randomly selected) data point at each iteration, yet without introducing bias to the algorithm's stationary distribution. However, the range of models for which PDMPs can be used, particularly with sub-sampling, is limited. We propose approximate simulation of PDMPs with sub-sampling for scalable sampling from posterior distributions. The approximation takes the form of an Euler approximation to the true PDMP dynamics, and involves using an estimate of the gradient of the log-posterior based on a data sub-sample. We thus call this class of algorithms stochastic-gradient PDMPs. Importantly, the trajectories of stochastic-gradient PDMPs are continuous and can leverage recent ideas for sampling from measures with continuous and atomic components. We show these methods are easy to implement, present results on their approximation error and demonstrate numerically that this class of algorithms has similar efficiency to, but is more robust than, stochastic gradient Langevin dynamics.

To analyze the topological properties of the given discrete data, one needs to consider a continuous transform called filtration. Persistent homology serves as a tool to track changes of homology in the filtration. The outcome of the topological analysis of data varies depending on the choice of filtration, making the selection of filtration crucial. Filtration learning is an attempt to find an optimal filtration that minimizes the loss function. Exact Multi-parameter Persistent Homology (EMPH) has been recently proposed, particularly for topological time-series analysis, that utilizes the exact formula of rank invariant instead of calculating it. In this paper, we propose a framework for filtration learning of EMPH. We formulate an optimization problem and propose an algorithm for solving the problem. We then apply the proposed algorithm to several classification problems. Particularly, we derive the exact formula of the gradient of the loss function with respect to the filtration parameter, which makes it possible to directly update the filtration without using automatic differentiation, significantly enhancing the learning process.

Agent-based models (ABM) provide an excellent framework for modeling outbreaks and interventions in epidemiology by explicitly accounting for diverse individual interactions and environments. However, these models are usually stochastic and highly parametrized, requiring precise calibration for predictive performance. When considering realistic numbers of agents and properly accounting for stochasticity, this high dimensional calibration can be computationally prohibitive. This paper presents a random forest based surrogate modeling technique to accelerate the evaluation of ABMs and demonstrates its use to calibrate an epidemiological ABM named CityCOVID via Markov chain Monte Carlo (MCMC). The technique is first outlined in the context of CityCOVID's quantities of interest, namely hospitalizations and deaths, by exploring dimensionality reduction via temporal decomposition with principal component analysis (PCA) and via sensitivity analysis. The calibration problem is then presented and samples are generated to best match COVID-19 hospitalization and death numbers in Chicago from March to June in 2020. These results are compared with previous approximate Bayesian calibration (IMABC) results and their predictive performance is analyzed showing improved performance with a reduction in computation.

"Accuracy-on-the-line" is a widely observed phenomenon in machine learning, where a model's accuracy on in-distribution (ID) and out-of-distribution (OOD) data is positively correlated across different hyperparameters and data configurations. But when does this useful relationship break down? In this work, we explore its robustness. The key observation is that noisy data and the presence of nuisance features can be sufficient to shatter the Accuracy-on-the-line phenomenon. In these cases, ID and OOD accuracy can become negatively correlated, leading to "Accuracy-on-the-wrong-line". This phenomenon can also occur in the presence of spurious (shortcut) features, which tend to overshadow the more complex signal (core, non-spurious) features, resulting in a large nuisance feature space. Moreover, scaling to larger datasets does not mitigate this undesirable behavior and may even exacerbate it. We formally prove a lower bound on Out-of-distribution (OOD) error in a linear classification model, characterizing the conditions on the noise and nuisance features for a large OOD error. We finally demonstrate this phenomenon across both synthetic and real datasets with noisy data and nuisance features.

In sampling tasks, it is common for target distributions to be known up to a normalising constant. However, in many situations, evaluating even the unnormalised distribution can be costly or infeasible. This issue arises in scenarios such as sampling from the Bayesian posterior for tall datasets and the 'doubly-intractable' distributions. In this paper, we begin by observing that seemingly different Markov chain Monte Carlo (MCMC) algorithms, such as the exchange algorithm, PoissonMH, and TunaMH, can be unified under a simple common procedure. We then extend this procedure into a novel framework that allows the use of auxiliary variables in both the proposal and acceptance-rejection steps. We develop the theory of the new framework, applying it to existing algorithms to simplify and extend their results. Several new algorithms emerge from this framework, with improved performance demonstrated on both synthetic and real datasets.

In recent years, transformer-based models have revolutionized deep learning, particularly in sequence modeling. To better understand this phenomenon, there is a growing interest in using Markov input processes to study transformers. However, our current understanding in this regard remains limited with many fundamental questions about how transformers learn Markov chains still unanswered. In this paper, we address this by focusing on first-order Markov chains and single-layer transformers, providing a comprehensive characterization of the learning dynamics in this context. Specifically, we prove that transformer parameters trained on next-token prediction loss can either converge to global or local minima, contingent on the initialization and the Markovian data properties, and we characterize the precise conditions under which this occurs. To the best of our knowledge, this is the first result of its kind highlighting the role of initialization. We further demonstrate that our theoretical findings are corroborated by empirical evidence. Based on these insights, we provide guidelines for the initialization of transformer parameters and demonstrate their effectiveness. Finally, we outline several open problems in this arena. Code is available at: https://github.com/Bond1995/Markov.

The European Space Agency's Copernicus Sentinel-1 (S-1) mission is a constellation of C-band synthetic aperture radar (SAR) satellites that provide unprecedented monitoring of the world's oceans. S-1's wave mode (WV) captures 20x20 km image patches at 5 m pixel resolution and is unaffected by cloud cover or time-of-day. The mission's open data policy has made SAR data easily accessible for a range of applications, but the need for manual image annotations is a bottleneck that hinders the use of machine learning methods. This study uses nearly 10 million WV-mode images and contrastive self-supervised learning to train a semantic embedding model called WV-Net. In multiple downstream tasks, WV-Net outperforms a comparable model that was pre-trained on natural images (ImageNet) with supervised learning. Experiments show improvements for estimating wave height (0.50 vs 0.60 RMSE using linear probing), estimating near-surface air temperature (0.90 vs 0.97 RMSE), and performing multilabel-classification of geophysical and atmospheric phenomena (0.96 vs 0.95 micro-averaged AUROC). WV-Net embeddings are also superior in an unsupervised image-retrieval task and scale better in data-sparse settings. Together, these results demonstrate that WV-Net embeddings can support geophysical research by providing a convenient foundation model for a variety of data analysis and exploration tasks.

Knowing the printer model used to print a given document may provide a crucial lead towards identifying counterfeits or conversely verifying the validity of a real document. Inkjet printers produce probabilistic droplet patterns that appear to be distinct for each printer model and as such we investigate the utilization of droplet characteristics including frequency domain features extracted from printed document scans for the classification of the underlying printer model. We collect and publish a dataset of high resolution document scans and show that our extracted features are informative enough to enable a neural network to distinguish not only the printer manufacturer, but also individual printer models.