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Tensor decompositions are powerful tools for analyzing multi-dimensional data in their original format. Besides tensor decompositions like Tucker and CP, Tensor SVD (t-SVD) which is based on the t-product of tensors is another extension of SVD to tensors that recently developed and has found numerous applications in analyzing high dimensional data. This paper offers a new insight into the t-Product and shows that this product is a block convolution of two tensors with periodic boundary conditions. Based on this viewpoint, we propose a new tensor-tensor product called the $\star_c{}\text{-Product}$ based on Block convolution with reflective boundary conditions. Using a tensor framework, this product can be easily extended to tensors of arbitrary order. Additionally, we introduce a tensor decomposition based on our $\star_c{}\text{-Product}$ for arbitrary order tensors. Compared to t-SVD, our new decomposition has lower complexity, and experiments show that it yields higher-quality results in applications such as classification and compression.

Large enterprises face a crucial imperative to achieve the Sustainable Development Goals (SDGs), especially goal 13, which focuses on combating climate change and its impacts. To mitigate the effects of climate change, reducing enterprise Scope 3 (supply chain emissions) is vital, as it accounts for more than 90\% of total emission inventories. However, tracking Scope 3 emissions proves challenging, as data must be collected from thousands of upstream and downstream suppliers.To address the above mentioned challenges, we propose a first-of-a-kind framework that uses domain-adapted NLP foundation models to estimate Scope 3 emissions, by utilizing financial transactions as a proxy for purchased goods and services. We compared the performance of the proposed framework with the state-of-art text classification models such as TF-IDF, word2Vec, and Zero shot learning. Our results show that the domain-adapted foundation model outperforms state-of-the-art text mining techniques and performs as well as a subject matter expert (SME). The proposed framework could accelerate the Scope 3 estimation at Enterprise scale and will help to take appropriate climate actions to achieve SDG 13.

We consider the degree-Rips construction from topological data analysis, which provides a density-sensitive, multiparameter hierarchical clustering algorithm. We analyze its stability to perturbations of the input data using the correspondence-interleaving distance, a metric for hierarchical clusterings that we introduce. Taking certain one-parameter slices of degree-Rips recovers well-known methods for density-based clustering, but we show that these methods are unstable. However, we prove that degree-Rips, as a multiparameter object, is stable, and we propose an alternative approach for taking slices of degree-Rips, which yields a one-parameter hierarchical clustering algorithm with better stability properties. We prove that this algorithm is consistent, using the correspondence-interleaving distance. We provide an algorithm for extracting a single clustering from one-parameter hierarchical clusterings, which is stable with respect to the correspondence-interleaving distance. And, we integrate these methods into a pipeline for density-based clustering, which we call Persistable. Adapting tools from multiparameter persistent homology, we propose visualization tools that guide the selection of all parameters of the pipeline. We demonstrate Persistable on benchmark datasets, showing that it identifies multi-scale cluster structure in data.

The development of technologies for causal inference with the privacy preservation of distributed data has attracted considerable attention in recent years. To address this issue, we propose a data collaboration quasi-experiment (DC-QE) that enables causal inference from distributed data with privacy preservation. In our method, first, local parties construct dimensionality-reduced intermediate representations from the private data. Second, they share intermediate representations, instead of private data for privacy preservation. Third, propensity scores were estimated from the shared intermediate representations. Finally, the treatment effects were estimated from propensity scores. Our method can reduce both random errors and biases, whereas existing methods can only reduce random errors in the estimation of treatment effects. Through numerical experiments on both artificial and real-world data, we confirmed that our method can lead to better estimation results than individual analyses. Dimensionality-reduction loses some of the information in the private data and causes performance degradation. However, we observed that in the experiments, sharing intermediate representations with many parties to resolve the lack of subjects and covariates, our method improved performance enough to overcome the degradation caused by dimensionality-reduction. With the spread of our method, intermediate representations can be published as open data to help researchers find causalities and accumulated as a knowledge base.

We study the online overlapping batch-means covariance estimator for Stochastic Gradient Descent (SGD) under Markovian sampling. We show that the convergence rates of the covariance estimator are $O\big(\sqrt{d}\,n^{-1/8}(\log n)^{1/4}\big)$ and $O\big(\sqrt{d}\,n^{-1/8}\big)$ under state-dependent and state-independent Markovian sampling, respectively, with $d$ representing dimensionality and $n$ denoting the number of observations or SGD iterations. Remarkably, these rates match the best-known convergence rate previously established for the independent and identically distributed ($\iid$) case by \cite{zhu2021online}, up to logarithmic factors. Our analysis overcomes significant challenges that arise due to Markovian sampling, leading to the introduction of additional error terms and complex dependencies between the blocks of the batch-means covariance estimator. Moreover, we establish the convergence rate for the first four moments of the $\ell_2$ norm of the error of SGD dynamics under state-dependent Markovian data, which holds potential interest as an independent result. To validate our theoretical findings, we provide numerical illustrations to derive confidence intervals for SGD when training linear and logistic regression models under Markovian sampling. Additionally, we apply our approach to tackle the intriguing problem of strategic classification with logistic regression, where adversaries can adaptively modify features during the training process to increase their chances of being classified in a specific target class.

Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable discretization space, and next perform a Galerkin approximation of the problem on that space. We investigate here how these approaches can be implemented in a non-intrusive way, in order to facilitate their dissemination within industrial codes or non-academic environments. We develop an abstract framework that covers a wide variety of MsFEMs for linear second-order partial differential equations. Non-intrusive MsFEM approaches are developed within the full generality of this framework, which may moreover be beneficial to steering software development and improving the theoretical understanding and analysis of MsFEMs.

We present Surjective Sequential Neural Likelihood (SSNL) estimation, a novel method for simulation-based inference in models where the evaluation of the likelihood function is not tractable and only a simulator that can generate synthetic data is available. SSNL fits a dimensionality-reducing surjective normalizing flow model and uses it as a surrogate likelihood function which allows for conventional Bayesian inference using either Markov chain Monte Carlo methods or variational inference. By embedding the data in a low-dimensional space, SSNL solves several issues previous likelihood-based methods had when applied to high-dimensional data sets that, for instance, contain non-informative data dimensions or lie along a lower-dimensional manifold. We evaluate SSNL on a wide variety of experiments and show that it generally outperforms contemporary methods used in simulation-based inference, for instance, on a challenging real-world example from astrophysics which models the magnetic field strength of the sun using a solar dynamo model.

Multispectral pedestrian detection achieves better visibility in challenging conditions and thus has a broad application in various tasks, for which both the accuracy and computational cost are of paramount importance. Most existing approaches treat RGB and infrared modalities equally, typically adopting two symmetrical CNN backbones for multimodal feature extraction, which ignores the substantial differences between modalities and brings great difficulty for the reduction of the computational cost as well as effective crossmodal fusion. In this work, we propose a novel and efficient framework named WCCNet that is able to differentially extract rich features of different spectra with lower computational complexity and semantically rearranges these features for effective crossmodal fusion. Specifically, the discrete wavelet transform (DWT) allowing fast inference and training speed is embedded to construct a dual-stream backbone for efficient feature extraction. The DWT layers of WCCNet extract frequency components for infrared modality, while the CNN layers extract spatial-domain features for RGB modality. This methodology not only significantly reduces the computational complexity, but also improves the extraction of infrared features to facilitate the subsequent crossmodal fusion. Based on the well extracted features, we elaborately design the crossmodal rearranging fusion module (CMRF), which can mitigate spatial misalignment and merge semantically complementary features of spatially-related local regions to amplify the crossmodal complementary information. We conduct comprehensive evaluations on KAIST and FLIR benchmarks, in which WCCNet outperforms state-of-the-art methods with considerable computational efficiency and competitive accuracy. We also perform the ablation study and analyze thoroughly the impact of different components on the performance of WCCNet.

We present ResMLP, an architecture built entirely upon multi-layer perceptrons for image classification. It is a simple residual network that alternates (i) a linear layer in which image patches interact, independently and identically across channels, and (ii) a two-layer feed-forward network in which channels interact independently per patch. When trained with a modern training strategy using heavy data-augmentation and optionally distillation, it attains surprisingly good accuracy/complexity trade-offs on ImageNet. We will share our code based on the Timm library and pre-trained models.

Recently pre-trained language representation models such as BERT have shown great success when fine-tuned on downstream tasks including information retrieval (IR). However, pre-training objectives tailored for ad-hoc retrieval have not been well explored. In this paper, we propose Pre-training with Representative wOrds Prediction (PROP) for ad-hoc retrieval. PROP is inspired by the classical statistical language model for IR, specifically the query likelihood model, which assumes that the query is generated as the piece of text representative of the "ideal" document. Based on this idea, we construct the representative words prediction (ROP) task for pre-training. Given an input document, we sample a pair of word sets according to the document language model, where the set with higher likelihood is deemed as more representative of the document. We then pre-train the Transformer model to predict the pairwise preference between the two word sets, jointly with the Masked Language Model (MLM) objective. By further fine-tuning on a variety of representative downstream ad-hoc retrieval tasks, PROP achieves significant improvements over baselines without pre-training or with other pre-training methods. We also show that PROP can achieve exciting performance under both the zero- and low-resource IR settings. The code and pre-trained models are available at //github.com/Albert-Ma/PROP.