随着优化软件的显着改进，几十年前似乎棘手的大规模问题的解决方案现在已成为日常任务。这将更多的现实应用程序纳入了优化器的范围。同时，解决优化问题通常是将解决方案付诸实践时较小的困难之一。一个主要的障碍是，可以将优化软件视为黑匣子，它可能会产生高质量的解决方案，但是当情况发生变化时，可以创建完全不同的解决方案，从而导致对优化解决方案的接受率低。这种可解释性和解释性的问题在其他领域（例如机器学习）引起了极大的关注，但在优化方面却不那么关注。在本文中，我们提出了一个优化框架，以得出本质上具有易于理解的解释性规则的解决方案，在哪些情况下应选择解决方案。我们专注于代表解释性规则的决策树，我们提出了整数编程公式以及一种启发式方法，以确保我们的方法即使在大规模问题上也适用。使用随机和现实世界数据的计算实验表明，固有的可解释性成本可能很小。

We study iterative methods for (two-stage) robust combinatorial optimization problems with discrete uncertainty. We propose a machine-learning-based heuristic to determine starting scenarios that provide strong lower bounds. To this end, we design dimension-independent features and train a Random Forest Classifier on small-dimensional instances. Experiments show that our method improves the solution process for larger instances than contained in the training set and also provides a feature importance-score which gives insights into the role of scenario properties.

Partial differential equations (PDEs) are important tools to model physical systems, and including them into machine learning models is an important way of incorporating physical knowledge. Given any system of linear PDEs with constant coefficients, we propose a family of Gaussian process (GP) priors, which we call EPGP, such that all realizations are exact solutions of this system. We apply the Ehrenpreis-Palamodov fundamental principle, which works like a non-linear Fourier transform, to construct GP kernels mirroring standard spectral methods for GPs. Our approach can infer probable solutions of linear PDE systems from any data such as noisy measurements, or initial and boundary conditions. Constructing EPGP-priors is algorithmic, generally applicable, and comes with a sparse version (S-EPGP) that learns the relevant spectral frequencies and works better for big data sets. We demonstrate our approach on three families of systems of PDE, the heat equation, wave equation, and Maxwell's equations, where we improve upon the state of the art in computation time and precision, in some experiments by several orders of magnitude.

Unbiased learning to rank (ULTR) studies the problem of mitigating various biases from implicit user feedback data such as clicks, and has been receiving considerable attention recently. A popular ULTR approach for real-world applications uses a two-tower architecture, where click modeling is factorized into a relevance tower with regular input features, and a bias tower with bias-relevant inputs such as the position of a document. A successful factorization will allow the relevance tower to be exempt from biases. In this work, we identify a critical issue that existing ULTR methods ignored - the bias tower can be confounded with the relevance tower via the underlying true relevance. In particular, the positions were determined by the logging policy, i.e., the previous production model, which would possess relevance information. We give both theoretical analysis and empirical results to show the negative effects on relevance tower due to such a correlation. We then propose three methods to mitigate the negative confounding effects by better disentangling relevance and bias. Empirical results on both controlled public datasets and a large-scale industry dataset show the effectiveness of the proposed approaches.

G-Enum histograms are a new fast and fully automated method for irregular histogram construction. By framing histogram construction as a density estimation problem and its automation as a model selection task, these histograms leverage the Minimum Description Length principle (MDL) to derive two different model selection criteria. Several proven theoretical results about these criteria give insights about their asymptotic behavior and are used to speed up their optimisation. These insights, combined to a greedy search heuristic, are used to construct histograms in linearithmic time rather than the polynomial time incurred by previous works. The capabilities of the proposed MDL density estimation method are illustrated with reference to other fully automated methods in the literature, both on synthetic and large real-world data sets.

Neural Radiance Fields (NeRFs) are emerging as a ubiquitous scene representation that allows for novel view synthesis. Increasingly, NeRFs will be shareable with other people. Before sharing a NeRF, though, it might be desirable to remove personal information or unsightly objects. Such removal is not easily achieved with the current NeRF editing frameworks. We propose a framework to remove objects from a NeRF representation created from an RGB-D sequence. Our NeRF inpainting method leverages recent work in 2D image inpainting and is guided by a user-provided mask. Our algorithm is underpinned by a confidence based view selection procedure. It chooses which of the individual 2D inpainted images to use in the creation of the NeRF, so that the resulting inpainted NeRF is 3D consistent. We show that our method for NeRF editing is effective for synthesizing plausible inpaintings in a multi-view coherent manner. We validate our approach using a new and still-challenging dataset for the task of NeRF inpainting.

Co-clustering is a class of unsupervised data analysis techniques that extract the existing underlying dependency structure between the instances and variables of a data table as homogeneous blocks. Most of those techniques are limited to variables of the same type. In this paper, we propose a mixed data co-clustering method based on a two-step methodology. In the first step, all the variables are binarized according to a number of bins chosen by the analyst, by equal frequency discretization in the numerical case, or keeping the most frequent values in the categorical case. The second step applies a co-clustering to the instances and the binary variables, leading to groups of instances and groups of variable parts. We apply this methodology on several data sets and compare with the results of a Multiple Correspondence Analysis applied to the same data.

Co-clustering is a data mining technique used to extract the underlying block structure between the rows and columns of a data matrix. Many approaches have been studied and have shown their capacity to extract such structures in continuous, binary or contingency tables. However, very little work has been done to perform co-clustering on mixed type data. In this article, we extend the latent block models based co-clustering to the case of mixed data (continuous and binary variables). We then evaluate the effectiveness of the proposed approach on simulated data and we discuss its advantages and potential limits.

We explore the abilities of two machine learning approaches for no-arbitrage interpolation of European vanilla option prices, which jointly yield the corresponding local volatility surface: a finite dimensional Gaussian process (GP) regression approach under no-arbitrage constraints based on prices, and a neural net (NN) approach with penalization of arbitrages based on implied volatilities. We demonstrate the performance of these approaches relative to the SSVI industry standard. The GP approach is proven arbitrage-free, whereas arbitrages are only penalized under the SSVI and NN approaches. The GP approach obtains the best out-of-sample calibration error and provides uncertainty quantification.The NN approach yields a smoother local volatility and a better backtesting performance, as its training criterion incorporates a local volatility regularization term.

Differentiable Search Indices (DSIs) encode a corpus of documents in the parameters of a model and use the same model to map queries directly to relevant document identifiers. Despite the strong performance of DSI models, deploying them in situations where the corpus changes over time is computationally expensive because reindexing the corpus requires re-training the model. In this work, we introduce DSI++, a continual learning challenge for DSI to incrementally index new documents while being able to answer queries related to both previously and newly indexed documents. Across different model scales and document identifier representations, we show that continual indexing of new documents leads to considerable forgetting of previously indexed documents. We also hypothesize and verify that the model experiences forgetting events during training, leading to unstable learning. To mitigate these issues, we investigate two approaches. The first focuses on modifying the training dynamics. Flatter minima implicitly alleviate forgetting, so we optimize for flatter loss basins and show that the model stably memorizes more documents (+12\%). Next, we introduce a generative memory to sample pseudo-queries for documents and supplement them during continual indexing to prevent forgetting for the retrieval task. Extensive experiments on novel continual indexing benchmarks based on Natural Questions (NQ) and MS MARCO demonstrate that our proposed solution mitigates forgetting by a significant margin. Concretely, it improves the average Hits@10 by $+21.1\%$ over competitive baselines for NQ and requires $6$ times fewer model updates compared to re-training the DSI model for incrementally indexing five corpora in a sequence.