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Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. The output of persistent homology is a persistence diagram -- a multiset of points supported on the upper half plane -- that is often used as a statistical summary of the topological features of data. In this paper, we study the random nature of persistent homology and estimate the density of expected persistence diagrams from observations using wavelets; we show that our wavelet-based estimator is optimal. Furthermore, we propose an estimator that offers a sparse representation of the expected persistence diagram that achieves near-optimality. We demonstrate the utility of our contributions in a machine learning task in the context of dynamical systems.

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Predicting the locations an individual will visit in the future is crucial for solving many societal issues like disease diffusion and reduction of pollution among many others. The models designed to tackle next-location prediction, however, require a significant amount of individual-level information to be trained effectively. Such data may be scarce or even unavailable in some geographic regions or peculiar scenarios (e.g., cold-start in recommendation systems). Moreover, the design of a next-location predictor able to generalize or geographically transfer knowledge is still an open research challenge. Recent advances in natural language processing have led to a rapid diffusion of Large Language Models (LLMs) which have shown good generalization and reasoning capabilities. These insights, coupled with the recent findings that LLMs are rich in geographical knowledge, allowed us to believe that these models can act as zero-shot next-location predictors. This paper evaluates the capabilities of many popular LLMs in this role, specifically Llama, GPT-3.5 and Mistral 7B. After designing a proper prompt, we tested the models on three real-world mobility datasets. The results show that LLMs can obtain accuracies up to 32.4%, a significant relative improvement of over 600% when compared to sophisticated DL models specifically designed for human mobility. Moreover, we show that other LLMs are unable to perform the task properly. To prevent positively biased results, we also propose a framework inspired by other studies to test data contamination. Finally, we explored the possibility of using LLMs as text-based explainers for next-location prediction showing that can effectively provide an explanation for their decision. Notably, 7B models provide more generic, but still reliable, explanations compared to larger counterparts. Code: github.com/ssai-trento/LLM-zero-shot-NL

In offline reinforcement learning, the challenge of out-of-distribution (OOD) is pronounced. To address this, existing methods often constrain the learned policy through policy regularization. However, these methods often suffer from the issue of unnecessary conservativeness, hampering policy improvement. This occurs due to the indiscriminate use of all actions from the behavior policy that generates the offline dataset as constraints. The problem becomes particularly noticeable when the quality of the dataset is suboptimal. Thus, we propose Adaptive Advantage-guided Policy Regularization (A2PR), obtaining high-advantage actions from an augmented behavior policy combined with VAE to guide the learned policy. A2PR can select high-advantage actions that differ from those present in the dataset, while still effectively maintaining conservatism from OOD actions. This is achieved by harnessing the VAE capacity to generate samples matching the distribution of the data points. We theoretically prove that the improvement of the behavior policy is guaranteed. Besides, it effectively mitigates value overestimation with a bounded performance gap. Empirically, we conduct a series of experiments on the D4RL benchmark, where A2PR demonstrates state-of-the-art performance. Furthermore, experimental results on additional suboptimal mixed datasets reveal that A2PR exhibits superior performance. Code is available at //github.com/ltlhuuu/A2PR.

Current autonomous driving technologies are being rolled out in geo-fenced areas with well-defined operation conditions such as time of operation, area, weather conditions and road conditions. In this way, challenging conditions as adverse weather, slippery road or densely-populated city centers can be excluded. In order to lift the geo-fenced restriction and allow a more dynamic availability of autonomous driving functions, it is necessary for the vehicle to autonomously perform an environment condition assessment in real time to identify when the system cannot operate safely and either stop operation or require the resting passenger to take control. In particular, adverse-weather challenges are a fundamental limitation as sensor performance degenerates quickly, prohibiting the use of sensors such as cameras to locate and monitor road signs, pedestrians or other vehicles. To address this issue, we train a deep learning model to identify outdoor weather and dangerous road conditions, enabling a quick reaction to new situations and environments. We achieve this by introducing an improved taxonomy and label hierarchy for a state-of-the-art adverse-weather dataset, relabelling it with a novel semi-automated labeling pipeline. Using the novel proposed dataset and hierarchy, we train RECNet, a deep learning model for the classification of environment conditions from a single RGB frame. We outperform baseline models by relative 16% in F1- Score, while maintaining a real-time capable performance of 20 Hz.

Unsupervised Continual Learning (UCL) is a burgeoning field in machine learning, focusing on enabling neural networks to sequentially learn tasks without explicit label information. Catastrophic Forgetting (CF), where models forget previously learned tasks upon learning new ones, poses a significant challenge in continual learning, especially in UCL, where labeled information of data is not accessible. CF mitigation strategies, such as knowledge distillation and replay buffers, often face memory inefficiency and privacy issues. Although current research in UCL has endeavored to refine data representations and address CF in streaming data contexts, there is a noticeable lack of algorithms specifically designed for unsupervised clustering. To fill this gap, in this paper, we introduce the concept of Unsupervised Continual Clustering (UCC). We propose Forward-Backward Knowledge Distillation for unsupervised Continual Clustering (FBCC) to counteract CF within the context of UCC. FBCC employs a single continual learner (the ``teacher'') with a cluster projector, along with multiple student models, to address the CF issue. The proposed method consists of two phases: Forward Knowledge Distillation, where the teacher learns new clusters while retaining knowledge from previous tasks with guidance from specialized student models, and Backward Knowledge Distillation, where a student model mimics the teacher's behavior to retain task-specific knowledge, aiding the teacher in subsequent tasks. FBCC marks a pioneering approach to UCC, demonstrating enhanced performance and memory efficiency in clustering across various tasks, outperforming the application of clustering algorithms to the latent space of state-of-the-art UCL algorithms.

We study asymptotic statistical inference in the space of bounded functions endowed with the supremums norm over an arbitrary metric space $S$ using a novel concept: Simultaneous COnfidence Region of Excursion (SCoRE) Sets. They simultaneously quantify the uncertainty of several lower and upper excursion sets of a target function. We investigate their connection to multiple hypothesis tests controlling the familywise error rate in the strong sense and show that they grant a unifying perspective on several statistical inference tools such as simultaneous confidence bands, quantification of uncertainties in level set estimation, for example, CoPE sets, and multiple hypothesis testing over $S$, for example, finding relevant differences or regions of equivalence within $S$. In particular, our abstract setting allows us to refine and reduce the assumptions in recent articles on CoPE sets and relevance and equivalence testing using the supremums norm.

Online experimentation with interference is a common challenge in modern applications such as e-commerce and adaptive clinical trials in medicine. For example, in online marketplaces, the revenue of a good depends on discounts applied to competing goods. Statistical inference with interference is widely studied in the offline setting, but far less is known about how to adaptively assign treatments to minimize regret. We address this gap by studying a multi-armed bandit (MAB) problem where a learner (e-commerce platform) sequentially assigns one of possible $\mathcal{A}$ actions (discounts) to $N$ units (goods) over $T$ rounds to minimize regret (maximize revenue). Unlike traditional MAB problems, the reward of each unit depends on the treatments assigned to other units, i.e., there is interference across the underlying network of units. With $\mathcal{A}$ actions and $N$ units, minimizing regret is combinatorially difficult since the action space grows as $\mathcal{A}^N$. To overcome this issue, we study a sparse network interference model, where the reward of a unit is only affected by the treatments assigned to $s$ neighboring units. We use tools from discrete Fourier analysis to develop a sparse linear representation of the unit-specific reward $r_n: [\mathcal{A}]^N \rightarrow \mathbb{R} $, and propose simple, linear regression-based algorithms to minimize regret. Importantly, our algorithms achieve provably low regret both when the learner observes the interference neighborhood for all units and when it is unknown. This significantly generalizes other works on this topic which impose strict conditions on the strength of interference on a known network, and also compare regret to a markedly weaker optimal action. Empirically, we corroborate our theoretical findings via numerical simulations.

Despite the recent progress in deep learning, most approaches still go for a silo-like solution, focusing on learning each task in isolation: training a separate neural network for each individual task. Many real-world problems, however, call for a multi-modal approach and, therefore, for multi-tasking models. Multi-task learning (MTL) aims to leverage useful information across tasks to improve the generalization capability of a model. This thesis is concerned with multi-task learning in the context of computer vision. First, we review existing approaches for MTL. Next, we propose several methods that tackle important aspects of multi-task learning. The proposed methods are evaluated on various benchmarks. The results show several advances in the state-of-the-art of multi-task learning. Finally, we discuss several possibilities for future work.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.

Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.

The cross-domain recommendation technique is an effective way of alleviating the data sparsity in recommender systems by leveraging the knowledge from relevant domains. Transfer learning is a class of algorithms underlying these techniques. In this paper, we propose a novel transfer learning approach for cross-domain recommendation by using neural networks as the base model. We assume that hidden layers in two base networks are connected by cross mappings, leading to the collaborative cross networks (CoNet). CoNet enables dual knowledge transfer across domains by introducing cross connections from one base network to another and vice versa. CoNet is achieved in multi-layer feedforward networks by adding dual connections and joint loss functions, which can be trained efficiently by back-propagation. The proposed model is evaluated on two real-world datasets and it outperforms baseline models by relative improvements of 3.56\% in MRR and 8.94\% in NDCG, respectively.

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