The theory of Koopman operators allows to deploy non-parametric machine learning algorithms to predict and analyze complex dynamical systems. Estimators such as principal component regression (PCR) or reduced rank regression (RRR) in kernel spaces can be shown to provably learn Koopman operators from finite empirical observations of the system's time evolution. Scaling these approaches to very long trajectories is a challenge and requires introducing suitable approximations to make computations feasible. In this paper, we boost the efficiency of different kernel-based Koopman operator estimators using random projections (sketching). We derive, implement and test the new "sketched" estimators with extensive experiments on synthetic and large-scale molecular dynamics datasets. Further, we establish non asymptotic error bounds giving a sharp characterization of the trade-offs between statistical learning rates and computational efficiency. Our empirical and theoretical analysis shows that the proposed estimators provide a sound and efficient way to learn large scale dynamical systems. In particular our experiments indicate that the proposed estimators retain the same accuracy of PCR or RRR, while being much faster.
The shift from the understanding and prediction of processes to their optimization offers great benefits to businesses and other organizations. Precisely timed process interventions are the cornerstones of effective optimization. Prescriptive process monitoring (PresPM) is the sub-field of process mining that concentrates on process optimization. The emerging PresPM literature identifies state-of-the-art methods, causal inference (CI) and reinforcement learning (RL), without presenting a quantitative comparison. Most experiments are carried out using historical data, causing problems with the accuracy of the methods' evaluations and preempting online RL. Our contribution consists of experiments on timed process interventions with synthetic data that renders genuine online RL and the comparison to CI possible, and allows for an accurate evaluation of the results. Our experiments reveal that RL's policies outperform those from CI and are more robust at the same time. Indeed, the RL policies approach perfect policies. Unlike CI, the unaltered online RL approach can be applied to other, more generic PresPM problems such as next best activity recommendations. Nonetheless, CI has its merits in settings where online learning is not an option.
The process of adapting or repurposing manga pages is a time-consuming task that requires manga artists to manually work on every single screentone region and apply new patterns to create novel screentones across multiple panels. To address this issue, we propose an automatic manga rescreening pipeline that aims to minimize the human effort involved in manga adaptation. Our pipeline automatically recognizes screentone regions and generates novel screentones with newly specified characteristics (e.g., intensity or type). Existing manga generation methods have limitations in understanding and synthesizing complex tone- or intensity-varying regions. To overcome these limitations, we propose a novel interpretable representation of screentones that disentangles their intensity and type features, enabling better recognition and synthesis of screentones. This interpretable screentone representation reduces ambiguity in recognizing intensity-varying regions and provides fine-grained controls during screentone synthesis by decoupling and anchoring the type or the intensity feature. Our proposed method is demonstrated to be effective and convenient through various experiments, showcasing the superiority of the newly proposed pipeline with the interpretable screentone representations.
Dynamic Time Warping (DTW) is a popular time series distance measure that aligns the points in two series with one another. These alignments support warping of the time dimension to allow for processes that unfold at differing rates. The distance is the minimum sum of costs of the resulting alignments over any allowable warping of the time dimension. The cost of an alignment of two points is a function of the difference in the values of those points. The original cost function was the absolute value of this difference. Other cost functions have been proposed. A popular alternative is the square of the difference. However, to our knowledge, this is the first investigation of both the relative impacts of using different cost functions and the potential to tune cost functions to different tasks. We do so in this paper by using a tunable cost function {\lambda}{\gamma} with parameter {\gamma}. We show that higher values of {\gamma} place greater weight on larger pairwise differences, while lower values place greater weight on smaller pairwise differences. We demonstrate that training {\gamma} significantly improves the accuracy of both the DTW nearest neighbor and Proximity Forest classifiers.
X-ray time-resolved tomography is one of the most popular X-ray techniques to probe dynamics in three dimensions (3D). Recent developments in time-resolved tomography opened the possibility of recording kilohertz-rate 3D movies. However, tomography requires rotating the sample with respect to the X-ray beam, which prevents characterization of faster structural dynamics. Here, we present megahertz (MHz) X-ray multi-projection imaging (MHz-XMPI), a technique capable of recording volumetric information at MHz rates and micrometer resolution without scanning the sample. We achieved this by harnessing the unique megahertz pulse structure and intensity of the European X-ray Free-electron Laser with a combination of novel detection and reconstruction approaches that do not require sample rotations. Our approach enables generating multiple X-ray probes that simultaneously record several angular projections for each pulse in the megahertz pulse burst. We provide a proof-of-concept demonstration of the MHz-XMPI technique's capability to probe 4D (3D+time) information on stochastic phenomena and non-reproducible processes three orders of magnitude faster than state-of-the-art time-resolved X-ray tomography, by generating 3D movies of binary droplet collisions. We anticipate that MHz-XMPI will enable in-situ and operando studies that were impossible before, either due to the lack of temporal resolution or because the systems were opaque (such as for MHz imaging based on optical microscopy).
Nowadays, there are many diffusion and autoregressive models that show impressive results for generating images from text and other input domains. However, these methods are not intended for ultra-high-resolution image synthesis. Vector graphics are devoid of this disadvantage, so the generation of images in this format looks very promising. Instead of generating vector images directly, you can first synthesize a raster image and then apply vectorization. Vectorization is the process of converting a raster image into a similar vector image using primitive shapes. Besides being similar, generated vector image is also required to contain the minimum number of shapes for rendering. In this paper, we focus specifically on machine learning-compatible vectorization methods. We are considering Mang2Vec, Deep Vectorization of Technical Drawings, DiffVG, and LIVE models. We also provide a brief overview of existing online methods. We also recall other algorithmic methods, Im2Vec and ClipGEN models, but they do not participate in the comparison, since there is no open implementation of these methods or their official implementations do not work correctly. Our research shows that despite the ability to directly specify the number and type of shapes, existing machine learning methods work for a very long time and do not accurately recreate the original image. We believe that there is no fast universal automatic approach and human control is required for every method.
Orthogonal time frequency space (OTFS) is a promising alternative to orthogonal frequency division multiplexing (OFDM) for high-mobility communications. We propose a novel multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system based on OTFS modulation. We begin by deriving new sensing and communication signal models for the proposed MIMO-OTFS ISAC system that explicitly capture inter-symbol interference (ISI) and inter-carrier interference (ICI) effects. We then develop a generalized likelihood ratio test (GLRT) based multi-target detection and delay-Doppler-angle estimation algorithm for MIMO-OTFS radar sensing that can simultaneously mitigate and exploit ISI/ICI effects, to prevent target masking and surpass standard unambiguous detection limits in range/velocity. Moreover, considering two operational modes (search/track), we propose an adaptive MIMO-OTFS ISAC transmission strategy. For the search mode, we introduce the concept of delay-Doppler (DD) multiplexing, enabling omnidirectional probing of the environment and large virtual array at the OTFS radar receiver. For the track mode, we pursue a directional transmission approach and design an OTFS ISAC optimization algorithm in spatial and DD domains, seeking the optimal trade-off between radar signal-to-noise ratio (SNR) and achievable rate. Simulation results verify the effectiveness of the proposed sensing algorithm and reveal valuable insights into OTFS ISAC trade-offs under varying communication channel characteristics.
The egocentric and exocentric viewpoints of a human activity look dramatically different, yet invariant representations to link them are essential for many potential applications in robotics and augmented reality. Prior work is limited to learning view-invariant features from paired synchronized viewpoints. We relax that strong data assumption and propose to learn fine-grained action features that are invariant to the viewpoints by aligning egocentric and exocentric videos in time, even when not captured simultaneously or in the same environment. To this end, we propose AE2, a self-supervised embedding approach with two key designs: (1) an object-centric encoder that explicitly focuses on regions corresponding to hands and active objects; (2) a contrastive-based alignment objective that leverages temporally reversed frames as negative samples. For evaluation, we establish a benchmark for fine-grained video understanding in the ego-exo context, comprising four datasets -- including an ego tennis forehand dataset we collected, along with dense per-frame labels we annotated for each dataset. On the four datasets, our AE2 method strongly outperforms prior work in a variety of fine-grained downstream tasks, both in regular and cross-view settings.
Recently, sequence learning methods have been applied to the problem of off-policy Reinforcement Learning, including the seminal work on Decision Transformers, which employs transformers for this task. Since transformers are parameter-heavy, cannot benefit from history longer than a fixed window size, and are not computed using recurrence, we set out to investigate the suitability of the S4 family of models, which are based on state-space layers and have been shown to outperform transformers, especially in modeling long-range dependencies. In this work we present two main algorithms: (i) an off-policy training procedure that works with trajectories, while still maintaining the training efficiency of the S4 model. (ii) An on-policy training procedure that is trained in a recurrent manner, benefits from long-range dependencies, and is based on a novel stable actor-critic mechanism. Our results indicate that our method outperforms multiple variants of decision transformers, as well as the other baseline methods on most tasks, while reducing the latency, number of parameters, and training time by several orders of magnitude, making our approach more suitable for real-world RL.
Bayesian Optimization (BO) is a class of surrogate-based, sample-efficient algorithms for optimizing black-box problems with small evaluation budgets. The BO pipeline itself is highly configurable with many different design choices regarding the initial design, surrogate model, and acquisition function (AF). Unfortunately, our understanding of how to select suitable components for a problem at hand is very limited. In this work, we focus on the definition of the AF, whose main purpose is to balance the trade-off between exploring regions with high uncertainty and those with high promise for good solutions. We propose Self-Adjusting Weighted Expected Improvement (SAWEI), where we let the exploration-exploitation trade-off self-adjust in a data-driven manner, based on a convergence criterion for BO. On the noise-free black-box BBOB functions of the COCO benchmarking platform, our method exhibits a favorable any-time performance compared to handcrafted baselines and serves as a robust default choice for any problem structure. The suitability of our method also transfers to HPOBench. With SAWEI, we are a step closer to on-the-fly, data-driven, and robust BO designs that automatically adjust their sampling behavior to the problem at hand.