Graphical models in extremes have emerged as a diverse and quickly expanding research area in extremal dependence modeling. They allow for parsimonious statistical methodology and are particularly suited for enforcing sparsity in high-dimensional problems. In this work, we provide the fundamental concepts of extremal graphical models and discuss recent advances in the field. Different existing perspectives on graphical extremes are presented in a unified way through graphical models for exponent measures. We discuss the important cases of nonparametric extremal graphical models on simple graph structures, and the parametric class of H\"usler--Reiss models on arbitrary undirected graphs. In both cases, we describe model properties, methods for statistical inference on known graph structures, and structure learning algorithms when the graph is unknown. We illustrate different methods in an application to flight delay data at US airports.
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Climate models are biased with respect to real world observations and usually need to be calibrated prior to impact studies. The suite of statistical methods that enable such calibrations is called bias correction (BC). However, current BC methods struggle to adjust for temporal biases, because they disregard the dependence between consecutive time-points. As a result, climate statistics with long-range temporal properties, such as heatwave duration and frequency, cannot be corrected accurately, making it more difficult to produce reliable impact studies on such climate statistics. In this paper, we offer a novel BC methodology to correct for temporal biases. This is made possible by i) re-thinking BC as a probability model rather than an algorithmic procedure, and ii) adapting state-of-the-art machine-learning (ML) probabilistic attention models to fit the BC task. With a case study of heatwave duration statistics in Abuja, Nigeria, and Tokyo, Japan, we show striking results compared to current climate model outputs and alternative BC methods.
Explaining outliers occurrence and mechanism of their occurrence can be extremely important in a variety of domains. Malfunctions, frauds, threats, in addition to being correctly identified, oftentimes need a valid explanation in order to effectively perform actionable counteracts. The ever more widespread use of sophisticated Machine Learning approach to identify anomalies make such explanations more challenging. We present the Decision Tree Outlier Regressor (DTOR), a technique for producing rule-based explanations for individual data points by estimating anomaly scores generated by an anomaly detection model. This is accomplished by first applying a Decision Tree Regressor, which computes the estimation score, and then extracting the relative path associated with the data point score. Our results demonstrate the robustness of DTOR even in datasets with a large number of features. Additionally, in contrast to other rule-based approaches, the generated rules are consistently satisfied by the points to be explained. Furthermore, our evaluation metrics indicate comparable performance to Anchors in outlier explanation tasks, with reduced execution time.
Accurate and precise climate projections are required for climate adaptation and mitigation, but Earth system models still exhibit great uncertainties. Several approaches have been developed to reduce the spread of climate projections and feedbacks, yet those methods cannot capture the non-linear complexity inherent in the climate system. Using a Transfer Learning approach, we show that Machine Learning can be used to optimally leverage and merge the knowledge gained from Earth system models simulations and historical observations to more accurately project global surface air temperature fields in the 21st century. We reach an uncertainty reduction of more than 50% with respect to state-of-the-art approaches. We give evidence that our novel method provides narrower projection uncertainty together with more accurate mean climate projections, urgently required for climate adaptation.
Diffusion-based generative models have emerged as powerful tools in the realm of generative modeling. Despite extensive research on denoising across various timesteps and noise levels, a conflict persists regarding the relative difficulties of the denoising tasks. While various studies argue that lower timesteps present more challenging tasks, others contend that higher timesteps are more difficult. To address this conflict, our study undertakes a comprehensive examination of task difficulties, focusing on convergence behavior and changes in relative entropy between consecutive probability distributions across timesteps. Our observational study reveals that denoising at earlier timesteps poses challenges characterized by slower convergence and higher relative entropy, indicating increased task difficulty at these lower timesteps. Building on these observations, we introduce an easy-to-hard learning scheme, drawing from curriculum learning, to enhance the training process of diffusion models. By organizing timesteps or noise levels into clusters and training models with descending orders of difficulty, we facilitate an order-aware training regime, progressing from easier to harder denoising tasks, thereby deviating from the conventional approach of training diffusion models simultaneously across all timesteps. Our approach leads to improved performance and faster convergence by leveraging the benefits of curriculum learning, while maintaining orthogonality with existing improvements in diffusion training techniques. We validate these advantages through comprehensive experiments in image generation tasks, including unconditional, class-conditional, and text-to-image generation.
In this thesis, we study problems at the interface of analysis and discrete mathematics. We discuss analogues of well known Hardy-type inequalities and Rearrangement inequalities on the lattice graphs $\mathbb{Z}^d$, with a particular focus on behaviour of sharp constants and optimizers.In the first half of the thesis, we analyse Hardy inequalities on $\mathbb{Z}^d$, first for $d=1$ and then for $d \geq 3$. We prove a sharp weighted Hardy inequality on integers with power weights of the form $n^\alpha$. This is done via two different methods, namely super-solution and Fourier method. We also use Fourier method to prove a weighted Hardy type inequality for higher order operators. After discussing the one dimensional case, we study the Hardy inequality in higher dimensions ($d \geq 3$). In particular, we compute the asymptotic behaviour of the sharp constant in the discrete Hardy inequality, as $d \rightarrow \infty$. This is done by converting the inequality into a continuous Hardy-type inequality on a torus for functions having zero average. These continuous inequalities are new and interesting in themselves. In the second half, we focus our attention on analogues of Rearrangement inequalities on lattice graphs. We begin by analysing the situation in dimension one. We define various notions of rearrangements and prove the corresponding Polya-Szeg\H{o} inequality. These inequalities are also applied to prove some weighted Hardy inequalities on integers. Finally, we study Rearrangement inequalities (Polya-Szeg\H{o}) on general graphs, with a particular focus on lattice graphs $\mathbb{Z}^d$, for $d \geq 2$. We develop a framework to study these inequalities, using which we derive concrete results in dimension two. In particular, these results develop connections between Polya-Szeg\H{o} inequality and various isoperimetric inequalities on graphs.
Trajectory prediction is an essential component in autonomous driving, particularly for collision avoidance systems. Considering the inherent uncertainty of the task, numerous studies have utilized generative models to produce multiple plausible future trajectories for each agent. However, most of them suffer from restricted representation ability or unstable training issues. To overcome these limitations, we propose utilizing the diffusion model to generate the distribution of future trajectories. Two cruxes are to be settled to realize such an idea. First, the diversity of intention is intertwined with the uncertain surroundings, making the true distribution hard to parameterize. Second, the diffusion process is time-consuming during the inference phase, rendering it unrealistic to implement in a real-time driving system. We propose an Intention-aware denoising Diffusion Model (IDM), which tackles the above two problems. We decouple the original uncertainty into intention uncertainty and action uncertainty and model them with two dependent diffusion processes. To decrease the inference time, we reduce the variable dimensions in the intention-aware diffusion process and restrict the initial distribution of the action-aware diffusion process, which leads to fewer diffusion steps. To validate our approach, we conduct experiments on the Stanford Drone Dataset (SDD) and ETH/UCY dataset. Our methods achieve state-of-the-art results, with an FDE of 13.83 pixels on the SDD dataset and 0.36 meters on the ETH/UCY dataset. Compared with the original diffusion model, IDM reduces inference time by two-thirds. Interestingly, our experiments further reveal that introducing intention information is beneficial in modeling the diffusion process of fewer steps.
For regression model selection under the maximum likelihood framework, we study the likelihood ratio confidence region for the regression parameter vector of a full regression model. We show that, when the confidence level increases with the sample size at a certain speed, with probability tending to one, the confidence region contains only vectors representing models having all active variables, including the parameter vector of the true model. This result leads to a consistent model selection criterion with a sparse maximum likelihood interpretation and certain advantages over popular information criteria. It also provides a large-sample characterization of models of maximum likelihood at different model sizes which shows that, for selection consistency, it suffices to consider only this small set of models.
Generative models, widely utilized in various applications, can often struggle with prompts corresponding to partial tokens. This struggle stems from tokenization, where partial tokens fall out of distribution during inference, leading to incorrect or nonsensical outputs. This paper examines a technique to alleviate the tokenization artifact on text completion in generative models, maintaining performance even in regular non-subword cases. The method, termed token alignment, involves backtracking to the last complete tokens and ensuring the model's generation aligns with the prompt. This approach showcases marked improvement across many partial token scenarios, including nuanced cases like space-prefix and partial indentation, with only a minor time increase. The technique and analysis detailed in this paper contribute to the continuous advancement of generative models in handling partial inputs, bearing relevance for applications like code completion and text autocompletion.
Edge Computing (EC) has gained significant traction in recent years, promising enhanced efficiency by integrating Artificial Intelligence (AI) capabilities at the edge. While the focus has primarily been on the deployment and inference of Machine Learning (ML) models at the edge, the training aspect remains less explored. This survey delves into Edge Learning (EL), specifically the optimization of ML model training at the edge. The objective is to comprehensively explore diverse approaches and methodologies in EL, synthesize existing knowledge, identify challenges, and highlight future trends. Utilizing Scopus' advanced search, relevant literature on EL was identified, revealing a concentration of research efforts in distributed learning methods, particularly Federated Learning (FL). This survey further provides a guideline for comparing techniques used to optimize ML for edge learning, along with an exploration of different frameworks, libraries, and simulation tools available for EL. In doing so, the paper contributes to a holistic understanding of the current landscape and future directions in the intersection of edge computing and machine learning, paving the way for informed comparisons between optimization methods and techniques designed for edge learning.
Human-in-the-loop aims to train an accurate prediction model with minimum cost by integrating human knowledge and experience. Humans can provide training data for machine learning applications and directly accomplish some tasks that are hard for computers in the pipeline with the help of machine-based approaches. In this paper, we survey existing works on human-in-the-loop from a data perspective and classify them into three categories with a progressive relationship: (1) the work of improving model performance from data processing, (2) the work of improving model performance through interventional model training, and (3) the design of the system independent human-in-the-loop. Using the above categorization, we summarize major approaches in the field, along with their technical strengths/ weaknesses, we have simple classification and discussion in natural language processing, computer vision, and others. Besides, we provide some open challenges and opportunities. This survey intends to provide a high-level summarization for human-in-the-loop and motivates interested readers to consider approaches for designing effective human-in-the-loop solutions.
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