Likelihood-based Imprecise Regression

We introduce a new approach to regression with imprecisely observed data, combining likelihood inference with ideas from imprecise probability theory, and thereby taking different kinds of uncertainty into account. The approach is very general and applicable to various kinds of imprecise data, not only to intervals. In the present paper, we propose a regression method based on this approach, where no parametric distributional assumption is needed and interval estimates of quantiles of the error distribution are used to identify plausible descriptions of the relationship of interest. Therefore, the proposed regression method is very robust. We apply our robust regression method to an interesting question in the social sciences. The analysis, based on survey data, yields a relatively imprecise result, reflecting the high amount of uncertainty inherent in the analyzed data set

3rd Workshop in Symbolic Data Analysis: book of abstracts

This workshop is the third regular meeting of researchers interested in Symbolic Data Analysis. The main aim of the event is to favor the meeting of people and the exchange of ideas from different fields - Mathematics, Statistics, Computer Science, Engineering, Economics, among others - that contribute to Symbolic Data Analysis

Archetypes for histogram-valued data

Il principale sviluppo innovativo del lavoro è quello di propone una estensione dell'analisi archetipale per dati ad istogramma. Per quanto concerne l'impianto metodologico nell'approccio all'analisi di dati ad istogramma, che sono di natura complessa, il presente lavora utilizza le intuizioni della "Symbolic Data Analysis" (SDA) e le relazioni intrinseche tra dati valutati ad intervallo e dati valutati ad istogramma. Dopo aver discusso la tecnica sviluppata in ambiente Matlab, il suo funzionamento e le sue proprietà su di un esempio di comodo, tale tecnica viene proposta, nella sezione applicativa, come strumento per effettuare una analisi di tipo "benchmarking" quantitativo. Nello specifico, si propongono i principali risultati ottenuti da una applicazione degli archetipi per dati ad istogramma ad un caso di benchmarking interno del sistema scolastico, utilizzando dati provenienti dal test INVALSI relativi all'anno scolastico 2015/2016. In questo contesto l'unità di analisi è considerata essere la singola scuola, definita operativamente attraverso le distribuzioni dei punteggi dei propri alunni valutate, congiuntamente, sotto forma di oggetti simbolici ad istogramma

A Robotic System for Learning Visually-Driven Grasp Planning (Dissertation Proposal)

We use findings in machine learning, developmental psychology, and neurophysiology to guide a robotic learning system\u27s level of representation both for actions and for percepts. Visually-driven grasping is chosen as the experimental task since it has general applicability and it has been extensively researched from several perspectives. An implementation of a robotic system with a gripper, compliant instrumented wrist, arm and vision is used to test these ideas. Several sensorimotor primitives (vision segmentation and manipulatory reflexes) are implemented in this system and may be thought of as the innate perceptual and motor abilities of the system. Applying empirical learning techniques to real situations brings up such important issues as observation sparsity in high-dimensional spaces, arbitrary underlying functional forms of the reinforcement distribution and robustness to noise in exemplars. The well-established technique of non-parametric projection pursuit regression (PPR) is used to accomplish reinforcement learning by searching for projections of high-dimensional data sets that capture task invariants. We also pursue the following problem: how can we use human expertise and insight into grasping to train a system to select both appropriate hand preshapes and approaches for a wide variety of objects, and then have it verify and refine its skills through trial and error. To accomplish this learning we propose a new class of Density Adaptive reinforcement learning algorithms. These algorithms use statistical tests to identify possibly interesting regions of the attribute space in which the dynamics of the task change. They automatically concentrate the building of high resolution descriptions of the reinforcement in those areas, and build low resolution representations in regions that are either not populated in the given task or are highly uniform in outcome. Additionally, the use of any learning process generally implies failures along the way. Therefore, the mechanics of the untrained robotic system must be able to tolerate mistakes during learning and not damage itself. We address this by the use of an instrumented, compliant robot wrist that controls impact forces

Towards Handling Uncertainty-at-Source in AI – A Review and Next Steps for Interval Regression

Most of statistics and AI draw insights through modelling discord or variance between sources (i.e., inter-source) of information. Increasingly however, research is focusing on uncertainty arising at the level of individual measurements (i.e., within- or intra-source), such as for a given sensor output or human response. Here, adopting intervals rather than numbers as the fundamental data-type provides an efficient, powerful, yet challenging way forward—offering systematic capture of uncertainty-at-source, increasing informational capacity, and ultimately potential for additional insight. Following progress in the capture of interval-valued data in particular from human participants, conducting machine learning directly upon intervals is a crucial next step. This paper focuses on linear regression for interval-valued data as a recent growth area, providing an essential foundation for broader use of intervals in AI. We conduct an in-depth analysis of state-of-the-art methods, elucidating their behaviour, advantages, and pitfalls when applied to synthetic and real-world data sets with different properties. Specific emphasis is given to the challenge of preserving mathematical coherence, i.e., models maintain fundamental mathematical properties of intervals. In support of real-world applicability of the regression methods, we introduce and demonstrate a novel visualization approach, the interval regression graph, or IRG , which effectively communicates the impact of both position and range of variables within the regression models—offering a leap in their interpretability. Finally, the paper provides practical recommendations concerning regression-method choice for interval data and highlights remaining challenges and important next steps for developing AI with the capacity to handle uncertainty-at-source