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This paper studies a Group Influence with Minimum cost which aims to find a seed set with smallest cost that can influence all target groups, where each user is associated with a cost and a group is influenced if the total score of the influenced users belonging to the group is at least a certain threshold. As the group-influence function is neither submodular nor supermodular, theoretical bounds on the quality of solutions returned by the well-known greedy approach may not be guaranteed. To address this challenge, we propose a bi-criteria polynomial-time approximation algorithm with high certainty. At the heart of the algorithm is a novel group reachable reverse sample concept, which helps speed up the estimation of the group influence function. Finally, extensive experiments conducted on real social networks show that our proposed algorithm outperform the state-of-the-art algorithms in terms of the objective value and the running time.

With an increasing amount of data in the art world, discovering artists and artworks suitable to collectors' tastes becomes a challenge. It is no longer enough to use visual information, as contextual information about the artist has become just as important in contemporary art. In this work, we present a generic Natural Language Processing framework (called ArtLM) to discover the connections among contemporary artists based on their biographies. In this approach, we first continue to pre-train the existing general English language models with a large amount of unlabelled art-related data. We then fine-tune this new pre-trained model with our biography pair dataset manually annotated by a team of professionals in the art industry. With extensive experiments, we demonstrate that our ArtLM achieves 85.6% accuracy and 84.0% F1 score and outperforms other baseline models. We also provide a visualisation and a qualitative analysis of the artist network built from ArtLM's outputs.

Time series is the most prevalent form of input data for educational prediction tasks. The vast majority of research using time series data focuses on hand-crafted features, designed by experts for predictive performance and interpretability. However, extracting these features is labor-intensive for humans and computers. In this paper, we propose an approach that utilizes irregular multivariate time series modeling with graph neural networks to achieve comparable or better accuracy with raw time series clickstreams in comparison to hand-crafted features. Furthermore, we extend concept activation vectors for interpretability in raw time series models. We analyze these advances in the education domain, addressing the task of early student performance prediction for downstream targeted interventions and instructional support. Our experimental analysis on 23 MOOCs with millions of combined interactions over six behavioral dimensions show that models designed with our approach can (i) beat state-of-the-art educational time series baselines with no feature extraction and (ii) provide interpretable insights for personalized interventions. Source code: //github.com/epfl-ml4ed/ripple/.

Although understanding and characterizing causal effects have become essential in observational studies, it is challenging when the confounders are high-dimensional. In this article, we develop a general framework $\textit{CausalEGM}$ for estimating causal effects by encoding generative modeling, which can be applied in both binary and continuous treatment settings. Under the potential outcome framework with unconfoundedness, we establish a bidirectional transformation between the high-dimensional confounders space and a low-dimensional latent space where the density is known (e.g., multivariate normal distribution). Through this, CausalEGM simultaneously decouples the dependencies of confounders on both treatment and outcome and maps the confounders to the low-dimensional latent space. By conditioning on the low-dimensional latent features, CausalEGM can estimate the causal effect for each individual or the average causal effect within a population. Our theoretical analysis shows that the excess risk for CausalEGM can be bounded through empirical process theory. Under an assumption on encoder-decoder networks, the consistency of the estimate can be guaranteed. In a series of experiments, CausalEGM demonstrates superior performance over existing methods for both binary and continuous treatments. Specifically, we find CausalEGM to be substantially more powerful than competing methods in the presence of large sample sizes and high dimensional confounders. The software of CausalEGM is freely available at //github.com/SUwonglab/CausalEGM.

Recent advances in safety-critical risk-aware control are predicated on apriori knowledge of the disturbances a system might face. This paper proposes a method to efficiently learn these disturbances online, in a risk-aware context. First, we introduce the concept of a Surface-at-Risk, a risk measure for stochastic processes that extends Value-at-Risk -- a commonly utilized risk measure in the risk-aware controls community. Second, we model the norm of the state discrepancy between the model and the true system evolution as a scalar-valued stochastic process and determine an upper bound to its Surface-at-Risk via Gaussian Process Regression. Third, we provide theoretical results on the accuracy of our fitted surface subject to mild assumptions that are verifiable with respect to the data sets collected during system operation. Finally, we experimentally verify our procedure by augmenting a drone's controller and highlight performance increases achieved via our risk-aware approach after collecting less than a minute of operating data.

We present a novel mathematical framework for computing the number of maintenance cycles in a system with critical and non-critical components, where "critical" (CR) means that the component's failure is fatal for the system's operation and renders any more repairs inapplicable, whereas "noncritical" (NC) means that the component can undergo corrective maintenance (replacement or minimal repair) whenever it fails, provided that the CR component is still in operation. Whenever the NC component fails, the CR component can optionally be preventively replaced. We extend traditional renewal theory (whether classical or generalized) for various maintenance scenarios for a system composed of one CR and one NC component in order to compute the average number of renewals of NC under the restriction ("bound") necessitated by CR. We also develop approximations in closed form for the proposed "bounded" renewal functions. We validate our formulas by simulations on a variety of component lifetime distributions, including actual lifetime distributions of wind turbine components.

The citation network of patents citing prior art arises from the legal obligation of patent applicants to properly disclose their invention. One way to study the relationship between current patents and their antecedents is by analyzing the similarity between the textual elements of patents. Patent similarity indicators have been constantly decreasing since the mid-70s. The aim of this work is to investigate the drivers of this downward trend through a general additive model and contextually propose a computationally efficient way to derive the similarity scores across pairs of patent citations leveraging on state-of-the-art tools in Natural Language Processing. We found that by using this non-linear modelling technique we are able to distinguish between distinct, temporally varying drivers of the patent similarity levels that accounts for more variation in the data ($R^2\sim 18\%$) in comparison to the previous literature. Moreover, with such corrections in place, we conclude that the trend in similarity shows a different pattern than the one presented in previous studies.

In this paper, we study an additive model where the response variable is Hilbert-space-valued and predictors are multivariate Euclidean, and both are possibly imperfectly observed. Considering Hilbert-space-valued responses allows to cover Euclidean, compositional, functional and density-valued variables. By treating imperfect responses, we can cover functional variables taking values in a Riemannian manifold and the case where only a random sample from a density-valued response is available. This treatment can also be applied in semiparametric regression. Dealing with imperfect predictors allows us to cover various principal component and singular component scores obtained from Hilbert-space-valued variables. For the estimation of the additive model having such variables, we use the smooth backfitting method. We provide full non-asymptotic and asymptotic properties of our regression estimator and present its wide applications via several simulation studies and real data applications.

Proper allocation of law enforcement resources remains a critical issue in crime prediction and prevention that operates by characterizing spatially aggregated crime activities and a multitude of predictor variables of interest. Despite the critical nature of proper resource allocation for mental health incidents, there has been little progress in statistical modeling of the geo-spatial nature of mental health events in Little Rock, Arkansas. In this article, we provide insights into the spatial nature of mental health data from Little Rock, Arkansas between 2015 and 2018, under a supervised spatial modeling framework while extending the popular risk terrain modeling (Caplan et al., 2011, 2015; Drawve, 2016) approach. We provide evidence of spatial clustering and identify the important features influencing such heterogeneity via a spatially informed hierarchy of generalized linear models, spatial regression models and a tree based method, viz., Poisson regression, spatial Durbin error model, Manski model and Random Forest. The insights obtained from these different models are presented here along with their relative predictive performances. The inferential tools developed here can be used in a broad variety of spatial modeling contexts and have the potential to aid both law enforcement agencies and the city in properly allocating resources.

This article develops a convex description of a classical or quantum learner's or agent's state of knowledge about its environment, presented as a convex subset of a commutative R-algebra. With caveats, this leads to a generalization of certain semidefinite programs in quantum information (such as those describing the universal query algorithm dual to the quantum adversary bound, related to optimal learning or control of the environment) to the classical and faulty-quantum setting, which would not be possible with a naive description via joint probability distributions over environment and internal memory. More philosophically, it also makes an interpretation of the set of reduced density matrices as "states of knowledge" of an observer of its environment, related to these techniques, more explicit. As another example, I describe and solve a formal differential equation of states of knowledge in that algebra, where an agent obtains experimental data in a Poissonian process, and its state of knowledge evolves as an exponential power series. However, this framework currently lacks impressive applications, and I post it in part to solicit feedback and collaboration on those. In particular, it may be possible to develop it into a new framework for the design of experiments, e.g. the problem of finding maximally informative questions to ask human labelers or the environment in machine-learning problems. The parts of the article not related to quantum information don't assume knowledge of it.