This paper is generally well written and clear, albeit targeting readers with formal backgrounds. The quality of the paper seems high in terms of its formal claims. The proposed mechanism is remarkable simple, making this an attractive approach. I really like the idea behind not making learning explicit (as opposed to rule induction for example). I have three main concerns about this paper: - In general it is very close to Juba's 2012 work [1].

From South Juba to Entebbe, from Marrakesh to Accra, on the cusp of technology in Africa, the need for responsible AI development and ethical data practices has never been more pressing. As technology continues to advance and shape the global economy, Africa is taking steps toward positioning itself as a leader in Artificial Intelligence (AI). Investments and innovations in AI are on the rise across the continent, with a growing number of countries beginning to develop policies and strategies to harness the power of this transformative technology. Although only a few countries have officially adopted AI strategies and policies, many more are actively working towards defining their AI policies. As philosopher and economist Amartya Sen noted, 'Development requires the removal of major sources of unfreedom that leave people with little choice and little opportunity of exercising their reasoned agency.'

Linear regression is a technique frequently used in statistical and data analysis. The task for standard linear regression is to fit a linear relationship among variables in a data set. Often, the goal is to find the most parsimonious model that can describe the majority of the data. In this work, we consider the situation where only a small portion of the data can be accurately modeled using linear regression. More generally, in many kinds of real-world data, portions of the data of significant size can be predicted significantly more accurately than by the best linear model for the overall data distribution: Rosenfeld et al. (2015) showed that there are attributes that are significant risk factors for gastrointestinal cancer in certain subpopulations, but not in the overall population. Hainline et al. (2019) demonstrated that a variety of standard (real-world) regression benchmarks have portions that are fit significantly better by a different linear model than the best model for the overall data set; Calderon et al. (2020) presented further, similar findings. We will consider cases where linear regression fits well when the data set is conditioned on a simple condition, which is unknown to us. We study the task of finding such a linear model, together with a formula on the data attributes describing the condition, i.e., the portion of the data for which the linear model is accurate. This problem was introduced by Juba (2017), who gave an algorithm for conditional sparse linear regression, using the maximum residual as the objective.

Juba recently proposed a formulation of learning abductive reasoning from examples, in which both the relative plausibility of various explanations, as well as which explanations are valid, are learned directly from data. The main shortcoming of this formulation of the task is that it assumes access to full-information (i.e., fully specified) examples; relatedly, it offers no role for declarative background knowledge, as such knowledge is rendered redundant in the abduction task by complete information. In this work we extend the formulation to utilize such partially specified examples, along with declarative background knowledge about the missing data. We show that it is possible to use implicitly learned rules together with the explicitly given declarative knowledge to support hypotheses in the course of abduction. We also show how to use knowledge in the form of graphical causal models to refine the proposed hypotheses. Finally, we observe that when a small explanation exists, it is possible to obtain a much-improved guarantee in the challenging exception-tolerant setting. Such small, human-understandable explanations are of particular interest for potential applications of the task.

Our work extends Juba’s formulation of learning abductive reasoning from examples, in which both the relative plausibility of various explanations, as well as which explanations are valid, are learned directly from data. We extend the formulation to consider partially observed examples, along with declarative background knowledge about the missing data. We show that it is possible to use implicitly learned rules together with the explicitly given declarative knowledge to support hypotheses in the course of abduction. We observe that when a small explanation exists, it is possible to obtain a much-improved guarantee in the challenging exception-tolerant setting.

In this case, we would be interested used in biological and social sciences to predict events and to in identifying a segment of the population for which describe possible relationships between variables. When addressing a linear rule is highly predictive of the price of certain cars, the task of prediction, machine learning and statistics whereas this linear rule may not provide a good prediction commonly focus on capturing the vast majority of data, overall in the larger population. Let us imagine that for this occasionally ignoring a segment of the population as "outliers" data set, and for a target fraction of the population, we found or "noise," which could be helpful to better understand a simple rule that describes the subpopulation, along with the data. Previous work by Juba (2016) gave an algorithm its linear fit.

Inference from an observed or hypothesized condition to a plausible cause or explanation for this condition is known as abduction. For many tasks, the acquisition of the necessary knowledge by machine learning has been widely found to be highly effective. However, the semantics of learned knowledge are weaker than the usual classical semantics, and this necessitates new formulations of many tasks. We focus on a recently introduced formulation of the abductive inference task that is thus adapted to the semantics of machine learning. A key problem is that we cannot expect that our causes or explanations will be perfect, and they must tolerate some error due to the world being more complicated than our formalization allows. This is a version of the qualification problem, and in machine learning, this is known as agnostic learning. In the work by Juba that introduced the task of learning to make abductive inferences, an algorithm is given for producing k-DNF explanations that tolerates such exceptions: if the best possible k-DNF explanation fails to justify the condition with probability ε, then the algorithm is promised to find a k-DNF explanation that fails to justify the condition with probability at most O(nkε), where n is the number of propositional attributes used to describe the domain. Here, we present an improved algorithm for this task. When the best k- DNF fails with probability ε, our algorithm finds a k-DNF that fails with probability at most O ̃(nk/2ε) (i.e., suppressing logarithmic factors in n and 1/ε). We also examine the empirical advantage of this new algorithm over the previous algorithm in two test domains, one of explaining conditions generated by a “noisy” k-DNF rule, and another of explaining conditions that are actually generated by a linear threshold rule.

That's how Hassan Yakub, al-Shabab's most senior leader in Somalia's Galgaduud region, responded when I requested that we use a drone to film his fighters at one of the armed group's training camps. Over the past few years, drone strikes have killed dozens of al-Shabab fighters, including the group's former leader and at least 10 of its senior commanders. The last drone hit to target the al-Qaeda-linked group's leaders happened just a month ago, in the East African country's Lower Juba region. Al-Shabab fighters have been trained to hide from drones or, if the unmanned aircraft are low enough, to shoot them down. Our cameraman was also not enthusiastic about taking a drone to an area controlled by al-Shabab.