Tensor decompositions have become a central tool in data science, with applications in areas such as data analysis, signal processing, and machine learning. A key property of many tensor decompositions, such as the canonical polyadic decomposition, is identifiability: the factors are unique, up to trivial scaling and permutation ambiguities. This allows one to recover the groundtruth sources that generated the data. The Tucker decomposition (TD) is a central and widely used tensor decomposition model. However, it is in general not identifiable. In this paper, we study the identifiability of the nonnegative TD (nTD). By adapting and extending identifiability results of nonnegative matrix factorization (NMF), we provide uniqueness results for nTD. Our results require the nonnegative matrix factors to have some degree of sparsity (namely, satisfy the separability condition, or the sufficiently scattered condition), while the core tensor only needs to have some slices (or linear combinations of them) or unfoldings with full column rank (but does not need to be nonnegative). Under such conditions, we derive several procedures, using either unfoldings or slices of the input tensor, to obtain identifiable nTDs by minimizing the volume of unfoldings or slices of the core tensor.

The legal landscape encompasses a wide array of lawsuit types, presenting lawyers with challenges in delivering timely and accurate information to clients, particularly concerning critical aspects like potential imprisonment duration or financial repercussions. Compounded by the scarcity of legal experts, there's an urgent need to enhance the efficiency of traditional legal workflows. Recent advances in deep learning, especially Large Language Models (LLMs), offer promising solutions to this challenge. Leveraging LLMs' mathematical reasoning capabilities, we propose a novel approach integrating LLM-based methodologies with specially designed prompts to address precision requirements in legal Artificial Intelligence (LegalAI) applications. The proposed work seeks to bridge the gap between traditional legal practices and modern technological advancements, paving the way for a more accessible, efficient, and equitable legal system. To validate this method, we introduce a curated dataset tailored to precision-oriented LegalAI tasks, serving as a benchmark for evaluating LLM-based approaches. Extensive experimentation confirms the efficacy of our methodology in generating accurate numerical estimates within the legal domain, emphasizing the role of LLMs in streamlining legal processes and meeting the evolving demands of LegalAI.

In the realm of continual learning, the presence of noisy labels within data streams represents a notable obstacle to model reliability and fairness. We focus on the data stream scenario outlined in pertinent literature, characterized by fuzzy task boundaries and noisy labels. To address this challenge, we introduce a novel and intuitive sampling method called Noisy Test Debiasing (NTD) to mitigate noisy labels in evolving data streams and establish a fair and robust continual learning algorithm. NTD is straightforward to implement, making it feasible across various scenarios. Our experiments benchmark four datasets, including two synthetic noise datasets (CIFAR10 and CIFAR100) and real-world noise datasets (mini-WebVision and Food-101N). The results validate the efficacy of NTD for online continual learning in scenarios with noisy labels in data streams. Compared to the previous leading approach, NTD achieves a training speedup enhancement over two times while maintaining or surpassing accuracy levels. Moreover, NTD utilizes less than one-fifth of the GPU memory resources compared to previous leading methods.

Distributional reinforcement learning (DRL) has achieved empirical success in various domains. One of the core tasks in the field of DRL is distributional policy evaluation, which involves estimating the return distribution $\eta^\pi$ for a given policy $\pi$. The distributional temporal difference (TD) algorithm has been accordingly proposed, which is an extension of the temporal difference algorithm in the classic RL literature. In the tabular case, \citet{rowland2018analysis} and \citet{rowland2023analysis} proved the asymptotic convergence of two instances of distributional TD, namely categorical temporal difference algorithm (CTD) and quantile temporal difference algorithm (QTD), respectively. In this paper, we go a step further and analyze the finite-sample performance of distributional TD. To facilitate theoretical analysis, we propose a non-parametric distributional TD algorithm (NTD). For a $\gamma$-discounted infinite-horizon tabular Markov decision process, we show that for NTD we need $\tilde{O}\left(\frac{1}{\varepsilon^{2p}(1-\gamma)^{2p+1}}\right)$ iterations to achieve an $\varepsilon$-optimal estimator with high probability, when the estimation error is measured by the $p$-Wasserstein distance. This sample complexity bound is minimax optimal (up to logarithmic factors) in the case of the $1$-Wasserstein distance. To achieve this, we establish a novel Freedman's inequality in Hilbert spaces, which would be of independent interest. In addition, we revisit CTD, showing that the same non-asymptotic convergence bounds hold for CTD in the case of the $p$-Wasserstein distance.

Neglected tropical diseases (NTDs) continue to affect the livelihood of individuals in countries in the Southeast Asia and Western Pacific region. These diseases have been long existing and have caused devastating health problems and economic decline to people in low- and middle-income (developing) countries. An estimated 1.7 billion of the world's population suffer one or more NTDs annually, this puts approximately one in five individuals at risk for NTDs. In addition to health and social impact, NTDs inflict significant financial burden to patients, close relatives, and are responsible for billions of dollars lost in revenue from reduced labor productivity in developing countries alone. There is an urgent need to better improve the control and eradication or elimination efforts towards NTDs. This can be achieved by utilizing machine learning tools to better the surveillance, prediction and detection program, and combat NTDs through the discovery of new therapeutics against these pathogens. This review surveys the current application of machine learning tools for NTDs and the challenges to elevate the state-of-the-art of NTDs surveillance, management, and treatment.

Nonnegative Tucker decomposition (NTD), a tensor decomposition model, has received increased interest in the recent years because of its ability to blindly extract meaningful patterns, in particular in Music Information Retrieval. Nevertheless, existing algorithms to compute NTD are mostly designed for the Euclidean loss. This work proposes a multiplicative updates algorithm to compute NTD with the beta-divergence loss, often considered a better loss for audio processing. We notably show how to implement efficiently the multiplicative rules using tensor algebra. Finally, we show on a music structure analysis task that unsupervised NTD fitted with beta-divergence loss outperforms earlier results obtained with the Euclidean loss.

A backdoor deep learning (DL) model behaves normally upon clean inputs but misbehaves upon trigger inputs as the backdoor attacker desires, posing severe consequences to DL model deployments. State-of-the-art defenses are either limited to specific backdoor attacks (source-agnostic attacks) or non-user-friendly in that machine learning (ML) expertise or expensive computing resources are required. This work observes that all existing backdoor attacks have an inevitable intrinsic weakness, non-transferability, that is, a trigger input hijacks a backdoored model but cannot be effective to another model that has not been implanted with the same backdoor. With this key observation, we propose non-transferability enabled backdoor detection (NTD) to identify trigger inputs for a model-under-test (MUT) during run-time.Specifically, NTD allows a potentially backdoored MUT to predict a class for an input. In the meantime, NTD leverages a feature extractor (FE) to extract feature vectors for the input and a group of samples randomly picked from its predicted class, and then compares similarity between the input and the samples in the FE's latent space. If the similarity is low, the input is an adversarial trigger input; otherwise, benign. The FE is a free pre-trained model privately reserved from open platforms. As the FE and MUT are from different sources, the attacker is very unlikely to insert the same backdoor into both of them. Because of non-transferability, a trigger effect that does work on the MUT cannot be transferred to the FE, making NTD effective against different types of backdoor attacks. We evaluate NTD on three popular customized tasks such as face recognition, traffic sign recognition and general animal classification, results of which affirm that NDT has high effectiveness (low false acceptance rate) and usability (low false rejection rate) with low detection latency.