We present a systematic analysis of estimation errors for a class of optimal transport based algorithms for filtering and data assimilation. Along the way, we extend previous error analyses of Brenier maps to the case of conditional Brenier maps that arise in the context of simulation based inference. We then apply these results in a filtering scenario to analyze the optimal transport filtering algorithm of Al-Jarrah et al. (2024, ICML). An extension of that algorithm along with numerical benchmarks on various non-Gaussian and high-dimensional examples are provided to demonstrate its effectiveness and practical potential.

Problem definition: Professional sports leagues may be suspended due to various reasons such as the recent COVID-19 pandemic. A critical question the league must address when re-opening is how to appropriately select a subset of the remaining games to conclude the season in a shortened time frame. Academic/practical relevance: Despite the rich literature on scheduling an entire season starting from a blank slate, concluding an existing season is quite different. Our approach attempts to achieve team rankings similar to that which would have resulted had the season been played out in full. Methodology: We propose a data-driven model which exploits predictive and prescriptive analytics to produce a schedule for the remainder of the season comprised of a subset of originally-scheduled games. Our model introduces novel rankings-based objectives within a stochastic optimization model, whose parameters are first estimated using a predictive model. We introduce a deterministic equivalent reformulation along with a tailored Frank-Wolfe algorithm to efficiently solve our problem, as well as a robust counterpart based on min-max regret. Results: We present simulation-based numerical experiments from previous National Basketball Association (NBA) seasons 2004--2019, and show that our models are computationally efficient, outperform a greedy benchmark that approximates a non-rankings-based scheduling policy, and produce interpretable results. Managerial implications: Our data-driven decision-making framework may be used to produce a shortened season with 25-50\% fewer games while still producing an end-of-season ranking similar to that of the full season, had it been played.

This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs), inspired by ideas from diffeomorphic matching and image registration. A theoretical analysis of the proposed method is presented, giving a priori error bounds in terms of the complexity of the model, the number of samples in the training set, and model misspecification. An extensive suite of numerical experiments further highlights the properties, strengths, and weaknesses of the method and extends its applicability to other tasks, such as conditional simulation and inference.

The diversity and Zipfian frequency distribution of natural language predicates in corpora leads to sparsity in Entailment Graphs (EGs) built by Open Relation Extraction (ORE). EGs are computationally efficient and explainable models of natural language inference, but as symbolic models, they fail if a novel premise or hypothesis vertex is missing at test-time. We present theory and methodology for overcoming such sparsity in symbolic models. First, we introduce a theory of optimal smoothing of EGs by constructing transitive chains. We then demonstrate an efficient, open-domain, and unsupervised smoothing method using an off-the-shelf Language Model to find approximations of missing premise predicates. This improves recall by 25.1 and 16.3 percentage points on two difficult directional entailment datasets, while raising average precision and maintaining model explainability. Further, in a QA task we show that EG smoothing is most useful for answering questions with lesser supporting text, where missing premise predicates are more costly. Finally, controlled experiments with WordNet confirm our theory and show that hypothesis smoothing is difficult, but possible in principle.

Global oil demand is rapidly increasing and is expected to reach 106.3 million barrels per day by 2040. Thus, it is vital for hydrocarbon extraction industries to forecast their production to optimize their operations and avoid losses. Big companies have realized that exploiting the power of deep learning (DL) and the massive amount of data from various oil wells for this purpose can save a lot of operational costs and reduce unwanted environmental impacts. In this direction, researchers have proposed models using conventional machine learning (ML) techniques for oil production forecasting. However, these techniques are inappropriate for this problem as they can not capture historical patterns found in time series data, resulting in inaccurate predictions. This research aims to overcome these issues by developing advanced data-driven regression models using sequential convolutions and long short-term memory (LSTM) units. Exhaustive analyses are conducted to select the optimal sequence length, model hyperparameters, and cross-well dataset formation to build highly generalized robust models. A comprehensive experimental study on Volve oilfield data validates the proposed models. It reveals that the LSTM-based sequence learning model can predict oil production better than the 1-D convolutional neural network (CNN) with mean absolute error (MAE) and R2 score of 111.16 and 0.98, respectively. It is also found that the LSTM-based model performs better than all the existing state-of-the-art solutions and achieves a 37% improvement compared to a standard linear regression, which is considered the baseline model in this work.

We introduce a priori Sobolev-space error estimates for the solution of nonlinear, and possibly parametric, PDEs using Gaussian process and kernel based methods. The primary assumptions are: (1) a continuous embedding of the reproducing kernel Hilbert space of the kernel into a Sobolev space of sufficient regularity; and (2) the stability of the differential operator and the solution map of the PDE between corresponding Sobolev spaces. The proof is articulated around Sobolev norm error estimates for kernel interpolants and relies on the minimizing norm property of the solution. The error estimates demonstrate dimension-benign convergence rates if the solution space of the PDE is smooth enough. We illustrate these points with applications to high-dimensional nonlinear elliptic PDEs and parametric PDEs. Although some recent machine learning methods have been presented as breaking the curse of dimensionality in solving high-dimensional PDEs, our analysis suggests a more nuanced picture: there is a trade-off between the regularity of the solution and the presence of the curse of dimensionality. Therefore, our results are in line with the understanding that the curse is absent when the solution is regular enough.

The growing societal dependence on social media and user generated content for news and information has increased the influence of unreliable sources and fake content, which muddles public discourse and lessens trust in the media. Validating the credibility of such information is a difficult task that is susceptible to confirmation bias, leading to the development of algorithmic techniques to distinguish between fake and real news. However, most existing methods are challenging to interpret, making it difficult to establish trust in predictions, and make assumptions that are unrealistic in many real-world scenarios, e.g., the availability of audiovisual features or provenance. In this work, we focus on fake news detection of textual content using interpretable features and methods. In particular, we have developed a deep probabilistic model that integrates a dense representation of textual news using a variational autoencoder and bi-directional Long Short-Term Memory (LSTM) networks with semantic topic-related features inferred from a Bayesian admixture model. Extensive experimental studies with 3 real-world datasets demonstrate that our model achieves comparable performance to state-of-the-art competing models while facilitating model interpretability from the learned topics. Finally, we have conducted model ablation studies to justify the effectiveness and accuracy of integrating neural embeddings and topic features both quantitatively by evaluating performance and qualitatively through separability in lower dimensional embeddings.

In fair division of indivisible goods,  ℓ-out-of-d maximin share (MMS) is the value that an agent can guarantee by partitioning the goods into d bundles and choosing the ℓ least preferred bundles. Most existing works aim to guarantee to all agents a constant fraction of their 1-out-of-n MMS. But this guarantee is sensitive to small perturbation in agents' cardinal valuations. We consider a more robust approximation notion, which depends only on the agents' ordinal rankings of bundles. We prove the existence of ℓ-out-of-⌊(ℓ + 1/2)n⌋ MMS allocations of goods for any integer ℓ ≥ 1, and present a polynomial-time algorithm that finds a 1-out-of-⌈3n/2⌉ MMS allocation when ℓ=1. We further develop an algorithm that provides a weaker ordinal approximation to MMS for any ℓ > 1.

Mobile apps offer users with functionalities and services by collecting information in various ways. Android app manifest file and privacy policy are documents that provide users with guidelines about what information type is being collected. However, the information types mentioned in these files are often abstract and do not include fine-grained details about information collected through user input fields in apps. Existing approaches only focus on Android API method calls which can reveal collected information types from a general category of well-defined names. However, these approaches are unable to identify the information types based on direct user input as a major source of private information. These information types contain more sensitive data compared to API retrieved information types. Moreover, developers can design user input fields that refer to any kind of information which can also vary among different apps. To address these problems, we propose to apply natural language processing techniques to Android layout code to extract information types associated with user input fields.

We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian processes. The proposed approach (1) provides a natural generalization of collocation kernel methods to nonlinear PDEs and IPs, (2) has guaranteed convergence with a path to compute error bounds in the PDE setting, and (3) inherits the state-of-the-art computational complexity of linear solvers for dense kernel matrices. The main idea of our method is to approximate the solution of a given PDE with a MAP estimator of a Gaussian process given the observation of the PDE at a finite number of collocation points. Although this optimization problem is infinite-dimensional, it can be reduced to a finite-dimensional one by introducing additional variables corresponding to the values of the derivatives of the solution at collocation points; this generalizes the representer theorem arising in Gaussian process regression. The reduced optimization problem has a quadratic loss and nonlinear constraints, and it is in turn solved with a variant of the Gauss-Newton method. The resulting algorithm (a) can be interpreted as solving successive linearizations of the nonlinear PDE, and (b) is found in practice to converge in a small number (two to ten) of iterations in experiments conducted on a range of PDEs. For IPs, while the traditional approach has been to iterate between the identifications of parameters in the PDE and the numerical approximation of its solution, our algorithm tackles both simultaneously. Experiments on nonlinear elliptic PDEs, Burgers' equation, a regularized Eikonal equation, and an IP for permeability identification in Darcy flow illustrate the efficacy and scope of our framework.