Do we really understand how machine classifies art styles? Historically, art is perceived and interpreted by human eyes and there are always controversial discussions over how people identify and understand art. Historians and general public tend to interpret the subject matter of art through the context of history and social factors. Style, however, is different from subject matter. Given the fact that Style does not correspond to the existence of certain objects in the painting and is mainly related to the form and can be correlated with features at different levels.(Ahmed Elgammal et al. 2018), which makes the identification and classification of the characteristics artwork's style and the "transition" - how it flows and evolves - remains as a challenge for both human and machine. In this work, a series of state-of-art neural networks and manifold learning algorithms are explored to unveil this intriguing topic: How does machine capture and interpret the flow of Art History?
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The graph Laplacian is a fundamental object in the analysis of and optimization on graphs. This operator can be extended to a simplicial complex $K$ and therefore offers a way to perform ``signal processing" on $p$-(co)chains of $K$. Recently, the concept of persistent Laplacian was proposed and studied for a pair of simplicial complexes $K\hookrightarrow L$ connected by an inclusion relation, further broadening the use of Laplace-based operators. In this paper, we expand the scope of the persistent Laplacian by generalizing it to a pair of simplicial complexes connected by a simplicial map $f: K \to L$. Such simplicial map setting arises frequently, e.g., when relating a coarsened simplicial representation with an original representation, or the case when the two simplicial complexes are spanned by different point sets i.e. cases in which it does not hold that $K\subset L$. However, the simplicial map setting is more challenging than the inclusion setting since the underlying algebraic structure is more complicated. We present a natural generalization of the persistent Laplacian to the simplicial setting. To shed insight on the structure behind it, as well as to develop an algorithm to compute it, we exploit the relationship between the persistent Laplacian and the Schur complement of a matrix. A critical step is to view the Schur complement as a functorial way of restricting a self-adjoint PSD operator to a given subspace. As a consequence, we prove that persistent Betti numbers of a simplicial map can be recovered by persistent Laplacians. We then propose an algorithm for finding the matrix representations of persistent Laplacians which in turn yields a new algorithm for computing persistent Betti numbers of a simplicial map. Finally, we study the persistent Laplacian on simplicial towers under simplicial maps and establish monotonicity results for their eigenvalues.
We propose a new approach to portfolio optimization that utilizes a unique combination of synthetic data generation and a CVaR-constraint. We formulate the portfolio optimization problem as an asset allocation problem in which each asset class is accessed through a passive (index) fund. The asset-class weights are determined by solving an optimization problem which includes a CVaR-constraint. The optimization is carried out by means of a Modified CTGAN algorithm which incorporates features (contextual information) and is used to generate synthetic return scenarios, which, in turn, are fed into the optimization engine. For contextual information we rely on several points along the U.S. Treasury yield curve. The merits of this approach are demonstrated with an example based on ten asset classes (covering stocks, bonds, and commodities) over a fourteen-and-half year period (January 2008-June 2022). We also show that the synthetic generation process is able to capture well the key characteristics of the original data, and the optimization scheme results in portfolios that exhibit satisfactory out-of-sample performance. We also show that this approach outperforms the conventional equal-weights (1/N) asset allocation strategy and other optimization formulations based on historical data only.
Federated learning methods, that is, methods that perform model training using data situated across different sources, whilst simultaneously not having the data leave their original source, are of increasing interest in a number of fields. However, despite this interest, the classes of models for which easily-applicable and sufficiently general approaches are available is limited, excluding many structured probabilistic models. We present a general yet elegant resolution to the aforementioned issue. The approach is based on adopting structured variational inference, an approach widely used in Bayesian machine learning, to the federated setting. Additionally, a communication-efficient variant analogous to the canonical FedAvg algorithm is explored. The effectiveness of the proposed algorithms are demonstrated, and their performance is compared on Bayesian multinomial regression, topic modelling, and mixed model examples.
Differential framing of issues can lead to divergent world views on important issues. This is especially true in domains where the information presented can reach a large audience, such as traditional and social media. Scalable and reliable measurement of such differential framing is an important first step in addressing them. In this work, based on the intuition that framing affects the tone and word choices in written language, we propose a framework for modeling the differential framing of issues through masked token prediction via large-scale fine-tuned language models (LMs). Specifically, we explore three key factors for our framework: 1) prompt generation methods for the masked token prediction; 2) methods for normalizing the output of fine-tuned LMs; 3) robustness to the choice of pre-trained LMs used for fine-tuning. Through experiments on a dataset of articles from traditional media outlets covering five diverse and politically polarized topics, we show that our framework can capture differential framing of these topics with high reliability.
We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy measurements. To quantify posterior uncertainty, we adopt Markov Chain Monte Carlo (MCMC) approaches for generating samples. To increase the efficiency of these approaches in high-dimension, we make use of local information about gradient and Hessian of the target potential, also via Hamiltonian Monte Carlo (HMC). Our target application is inferring the field of soil permeability processing observations of pore pressure, using a nonlinear PDE poromechanics model for predicting pressure from permeability. We compare the performance of different sampling approaches in this and other settings. We also investigate the effect of dimensionality and non-gaussianity of distributions on the performance of different sampling methods.
Neural networks are prone to overfitting and memorizing data patterns. To avoid over-fitting and enhance their generalization and performance, various methods have been suggested in the literature, including dropout, regularization, label smoothing, etc. One such method is augmentation which introduces different types of corruption in the data to prevent the model from overfitting and to memorize patterns present in the data. A sub-area of data augmentation is image mixing and deleting. This specific type of augmentation either deletes image regions or mixes two images to hide or make particular characteristics of images confusing for the network, forcing it to emphasize the overall structure of the object in an image. Models trained with this approach have proven to perform and generalize well compared to those trained without image mixing or deleting. An added benefit that comes with this method of training is robustness against image corruption. Due to its low computational cost and recent success, researchers have proposed many image mixing and deleting techniques. We furnish an in-depth survey of image mixing and deleting techniques and provide categorization via their most distinguishing features. We initiate our discussion with some fundamental relevant concepts. Next, we present essentials, such as each category's strengths and limitations, describing their working mechanism, basic formulations, and applications. We also discuss the general challenges and recommend possible future research directions for image mixing and deleting data augmentation techniques. Datasets and codes for evaluation are publicly available here.
As increasingly powerful generative AI systems are developed, the release method greatly varies. We propose a framework to assess six levels of access to generative AI systems: fully closed; gradual or staged access; hosted access; cloud-based or API access; downloadable access; and fully open. Each level, from fully closed to fully open, can be viewed as an option along a gradient. We outline key considerations across this gradient: release methods come with tradeoffs, especially around the tension between concentrating power and mitigating risks. Diverse and multidisciplinary perspectives are needed to examine and mitigate risk in generative AI systems from conception to deployment. We show trends in generative system release over time, noting closedness among large companies for powerful systems and openness among organizations founded on principles of openness. We also enumerate safety controls and guardrails for generative systems and necessary investments to improve future releases.
The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.
Deep learning-based semi-supervised learning (SSL) algorithms have led to promising results in medical images segmentation and can alleviate doctors' expensive annotations by leveraging unlabeled data. However, most of the existing SSL algorithms in literature tend to regularize the model training by perturbing networks and/or data. Observing that multi/dual-task learning attends to various levels of information which have inherent prediction perturbation, we ask the question in this work: can we explicitly build task-level regularization rather than implicitly constructing networks- and/or data-level perturbation-and-transformation for SSL? To answer this question, we propose a novel dual-task-consistency semi-supervised framework for the first time. Concretely, we use a dual-task deep network that jointly predicts a pixel-wise segmentation map and a geometry-aware level set representation of the target. The level set representation is converted to an approximated segmentation map through a differentiable task transform layer. Simultaneously, we introduce a dual-task consistency regularization between the level set-derived segmentation maps and directly predicted segmentation maps for both labeled and unlabeled data. Extensive experiments on two public datasets show that our method can largely improve the performance by incorporating the unlabeled data. Meanwhile, our framework outperforms the state-of-the-art semi-supervised medical image segmentation methods. Code is available at: //github.com/Luoxd1996/DTC
Deep learning models on graphs have achieved remarkable performance in various graph analysis tasks, e.g., node classification, link prediction and graph clustering. However, they expose uncertainty and unreliability against the well-designed inputs, i.e., adversarial examples. Accordingly, various studies have emerged for both attack and defense addressed in different graph analysis tasks, leading to the arms race in graph adversarial learning. For instance, the attacker has poisoning and evasion attack, and the defense group correspondingly has preprocessing- and adversarial- based methods. Despite the booming works, there still lacks a unified problem definition and a comprehensive review. To bridge this gap, we investigate and summarize the existing works on graph adversarial learning tasks systemically. Specifically, we survey and unify the existing works w.r.t. attack and defense in graph analysis tasks, and give proper definitions and taxonomies at the same time. Besides, we emphasize the importance of related evaluation metrics, and investigate and summarize them comprehensively. Hopefully, our works can serve as a reference for the relevant researchers, thus providing assistance for their studies. More details of our works are available at //github.com/gitgiter/Graph-Adversarial-Learning.
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