Over the last decades, the family of $\alpha$-stale distributions has proven to be useful for modelling in telecommunication systems. Particularly, in the case of radar applications, finding a fast and accurate estimation for the amplitude density function parameters appears to be very important. In this work, the maximum likelihood estimator (MLE) is proposed for parameters of the amplitude distribution. To do this, the amplitude data are \emph{projected} on the horizontal and vertical axes using two simple transformations. It is proved that the \emph{projected} data follow a zero-location symmetric $\alpha$-stale distribution for which the MLE can be computed quite fast. The average of computed MLEs based on two \emph{projections} is considered as estimator for parameters of the amplitude distribution. Performance of the proposed \emph{projection} method is demonstrated through simulation study and analysis of two sets of real radar data.

It has become common sense that transferring intrinsic information from teachers to the greatest extent can expedite a student's learning progress, especially in machine learning given versatile and powerful teacher models. Learning with their assistance has been coined knowledge distillation (KD) (Hinton et al., 2015; Lopez-Paz et al., 2015), a famous paradigm of knowledge transfer leading to remarkable empirical effectiveness in classification tasks across various downstream applications (Gou et al., 2021; Wang and Yoon, 2021; Gu et al., 2023b). The term distillation implies a belief that the inscrutable teacher(s) may possess useful yet complicated structural information, which we should be able to compress and inject into a compact one, i.e., the student model (Breiman and Shang, 1996; Buciluǎ et al., 2006; Li et al., 2014; Ba and Caruana, 2014; Allen-Zhu and Li, 2020). This has guided the community towards a line of knowledge transfer methods featuring the awareness of teacher training details or snapshots, such as the original training set, the intermediate activations, the last-layer logits (for a probabilistic classifier), the first-or second-order derivative or statistical information, and even task-specific knowledge (Hinton et al., 2015; Furlanello et al., 2018; Cho and Hariharan, 2019; Zhao et al., 2022; Romero et al., 2014; Zagoruyko and Komodakis, 2016;

Artificial intelligence experienced a technological breakthrough in science, industry, and everyday life in the recent few decades. The advancements can be credited to the ever-increasing availability and miniaturization of computational resources that resulted in exponential data growth. However, because of the insufficient amount of data in some cases, employing machine learning in solving complex tasks is not straightforward or even possible. As a result, machine learning with small data experiences rising importance in data science and application in several fields. The authors focus on interpreting the general term of "small data" and their engineering and industrial application role. They give a brief overview of the most important industrial applications of machine learning and small data. Small data is defined in terms of various characteristics compared to big data, and a machine learning formalism was introduced. Five critical challenges of machine learning with small data in industrial applications are presented: unlabeled data, imbalanced data, missing data, insufficient data, and rare events. Based on those definitions, an overview of the considerations in domain representation and data acquisition is given along with a taxonomy of machine learning approaches in the context of small data.

Causal discovery is becoming a key part in medical AI research. These methods can enhance healthcare by identifying causal links between biomarkers, demographics, treatments and outcomes. They can aid medical professionals in choosing more impactful treatments and strategies. In parallel, Large Language Models (LLMs) have shown great potential in identifying patterns and generating insights from text data. In this paper we investigate applying LLMs to the problem of determining the directionality of edges in causal discovery. Specifically, we test our approach on a deidentified set of Non Small Cell Lung Cancer(NSCLC) patients that have both electronic health record and genomic panel data. Graphs are validated using Bayesian Dirichlet estimators using tabular data. Our result shows that LLMs can accurately predict the directionality of edges in causal graphs, outperforming existing state-of-the-art methods. These findings suggests that LLMs can play a significant role in advancing causal discovery and help us better understand complex systems.

Language model (LM) prompting--a popular paradigm for solving NLP tasks-- has been shown to be susceptible to miscalibration and brittleness to slight prompt variations, caused by its discriminative prompting approach, i.e., predicting the label given the input. The framework is multivariate, as label descriptions allow us to seamlessly integrate additional contextual information about the labels to improve task performance. On various standard classification benchmarks, with six open-source LM families, we show that zero-shot classification with simple contextualization of the data source of the evaluation set consistently outperforms both zero-shot and few-shot baselines while improving robustness to prompt variations. Further, our approach enables personalizing classification in a zero-shot manner by incorporating author, subject, or reader information in the label descriptions. Language models, trained only on raw text, have been shown to perform new tasks simply by conditioning on a handful of demonstrations (Brown et al., 2020). Furthermore, ICL has been shown to be very sensitive to the choice of training examples, their order and format in the prompt (Lu et al., 2022; Sorensen et al., 2022) requiring major human effort to achieve optimal performance. In this work, we ask, "If the right demonstrations are challenging to find and only serve to implicitly prime the model, can we achieve the same performance zero-shot if we prime the language model explicitly in a robust way?" Our approach consists of two key ideas. First, most text classification methods follow a discriminative setup, which involves estimating the probability of the labels given the input, which can be sensitive to prompt or verbalizer variations. Instead, we use a generative setup, which involves estimating the probability of generating the input given different labels, which has been shown to have better worst-case performance (Min et al., 2022a).

Double-descent refers to the unexpected drop in test loss of a learning algorithm beyond an interpolating threshold with over-parameterization, which is not predicted by information criteria in their classical forms due to the limitations in the standard asymptotic approach. We update these analyses using the information risk minimization framework and provide Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for models learned by the Gibbs algorithm. Notably, the penalty terms for the Gibbs-based AIC and BIC correspond to specific information measures, i.e., symmetrized KL information and KL divergence. We extend this information-theoretic analysis to over-parameterized models by providing two different Gibbs-based BICs to compute the marginal likelihood of random feature models in the regime where the number of parameters $p$ and the number of samples $n$ tend to infinity, with $p/n$ fixed. Our experiments demonstrate that the Gibbs-based BIC can select the high-dimensional model and reveal the mismatch between marginal likelihood and population risk in the over-parameterized regime, providing new insights to understand double-descent.

Although linear and quadratic discriminant analysis are widely recognized classical methods, they can encounter significant challenges when dealing with non-Gaussian distributions or contaminated datasets. This is primarily due to their reliance on the Gaussian assumption, which lacks robustness. We first explain and review the classical methods to address this limitation and then present a novel approach that overcomes these issues. In this new approach, the model considered is an arbitrary Elliptically Symmetrical (ES) distribution per cluster with its own arbitrary scale parameter. This flexible model allows for potentially diverse and independent samples that may not follow identical distributions. By deriving a new decision rule, we demonstrate that maximum-likelihood parameter estimation and classification are simple, efficient, and robust compared to state-of-the-art methods.

Probabilistic principal component analysis (PPCA) is currently one of the most used statistical tools to reduce the ambient dimension of the data. From multidimensional scaling to the imputation of missing data, PPCA has a broad spectrum of applications ranging from science and engineering to quantitative finance. Despite this wide applicability in various fields, hardly any theoretical guarantees exist to justify the soundness of the maximum likelihood (ML) solution for this model. In fact, it is well known that the maximum likelihood estimation (MLE) can only recover the true model parameters up to a rotation. The main obstruction is posed by the inherent identifiability nature of the PPCA model resulting from the rotational symmetry of the parameterization. To resolve this ambiguity, we propose a novel approach using quotient topological spaces and in particular, we show that the maximum likelihood solution is consistent in an appropriate quotient Euclidean space. Furthermore, our consistency results encompass a more general class of estimators beyond the MLE. Strong consistency of the ML estimate and consequently strong covariance estimation of the PPCA model have also been established under a compactness assumption.

Segmentation has emerged as a fundamental field of computer vision and natural language processing, which assigns a label to every pixel/feature to extract regions of interest from an image/text. To evaluate the performance of segmentation, the Dice and IoU metrics are used to measure the degree of overlap between the ground truth and the predicted segmentation. In this paper, we establish a theoretical foundation of segmentation with respect to the Dice/IoU metrics, including the Bayes rule and Dice-/IoU-calibration, analogous to classification-calibration or Fisher consistency in classification. We prove that the existing thresholding-based framework with most operating losses are not consistent with respect to the Dice/IoU metrics, and thus may lead to a suboptimal solution. To address this pitfall, we propose a novel consistent ranking-based framework, namely RankDice/RankIoU, inspired by plug-in rules of the Bayes segmentation rule. Three numerical algorithms with GPU parallel execution are developed to implement the proposed framework in large-scale and high-dimensional segmentation. We study statistical properties of the proposed framework. We show it is Dice-/IoU-calibrated, and its excess risk bounds and the rate of convergence are also provided. The numerical effectiveness of RankDice/mRankDice is demonstrated in various simulated examples and Fine-annotated CityScapes, Pascal VOC and Kvasir-SEG datasets with state-of-the-art deep learning architectures.

Recent digital advances have popularized predictive maintenance (PMx), offering enhanced efficiency, automation, accuracy, cost savings, and independence in maintenance. Yet, it continues to face numerous limitations such as poor explainability, sample inefficiency of data-driven methods, complexity of physics-based methods, and limited generalizability and scalability of knowledge-based methods. This paper proposes leveraging Digital Twins (DTs) to address these challenges and enable automated PMx adoption at larger scales. While we argue that DTs have this transformative potential, they have not yet reached the level of maturity needed to bridge these gaps in a standardized way. Without a standard definition for such evolution, this transformation lacks a solid foundation upon which to base its development. This paper provides a requirement-based roadmap supporting standardized PMx automation using DT technologies. A systematic approach comprising two primary stages is presented. First, we methodically identify the Informational Requirements (IRs) and Functional Requirements (FRs) for PMx, which serve as a foundation from which any unified framework must emerge. Our approach to defining and using IRs and FRs to form the backbone of any PMx DT is supported by the track record of IRs and FRs being successfully used as blueprints in other areas, such as for product development within the software industry. Second, we conduct a thorough literature review spanning fields to determine the ways in which these IRs and FRs are currently being used within DTs, enabling us to point to the specific areas where further research is warranted to support the progress and maturation of requirement-based PMx DTs.