We show in this paper that all existing implementations of gradient boosting face the following statistical issue.

Under certain assumptions, frequently made for Bayes consistencyresults, we show that consistency in GeDTs and GeFs extend to any pattern of missing inputfeatures, ifmissing atrandom.

Insteadof (2), consider (Q 1 ,..., Q q ) = argmin Rubin, D. Statistics, pages Rubin, D. comment.

Only users who have already registered and completed age verification will be able to access the world's largest porn site. Pornhub is blocking itself in the United Kingdom on February 2, arguing that the country's age verification laws are ineffective, the company announced on Tuesday. As of February 2, only users who have already registered with Pornhub and completed age verification will be able to access the site. New users will not be able to register. The move comes after a new set of provisions aimed at keeping minors from viewing porn kicked in last July, requiring adults to submit to age-estimating face scans, ID document uploads, credit card checks, and more, in order to verify that they are not minors.

The following lemma states that each level set of the quadratic loss surface is a hyper-ellipsoid, providing another useful tool for the propositions given in this section. Lemma 2. The level set of the quadratic loss at ε is a hyper-ellipsoid defined by: (θ θ

This article proposes predictive economics as a distinct analytical perspective within economics, grounded in machine learning and centred on predictive accuracy rather than causal identification. Drawing on the instrumentalist tradition (Friedman), the explanation-prediction divide (Shmueli), and the contrast between modelling cultures (Breiman), we formalise prediction as a valid epistemological and methodological objective. Reviewing recent applications across economic subfields, we show how predictive models contribute to empirical analysis, particularly in complex or data-rich contexts. This perspective complements existing approaches and supports a more pluralistic methodology - one that values out-of-sample performance alongside interpretability and theoretical structure. Keywords: Predictive economics, Machine learning, Forecasting, Causal inference, Economic methodology 1. Introduction The evolution of economics has long been shaped by advances in analytical tools.

This study reinterprets a Monte Carlo simulation of students' perceived success with generative AI (GenAI) through a Kantian-axiomatic lens. Building on prior work, theme-level survey statistics Ease of Use and Learnability, System Efficiency and Learning Burden, and Perceived Complexity and Integration from a representative dataset are used to generate 10,000 synthetic scores per theme on the [1,5] Likert scale. The simulated outputs are evaluated against the axioms of dense linear order without endpoints (DLO): irreflexivity, transitivity, total comparability (connectedness), no endpoints (no greatest and no least; A4-A5), and density (A6). At the data level, the basic ordering axioms (A1-A3) are satisfied, whereas no-endpoints (A4-A5) and density (A6) fail as expected. Likert clipping introduces minimum and maximum observed values, and a finite, discretized sample need not contain a value strictly between any two distinct scores. These patterns are read not as methodological defects but as markers of an epistemological boundary. Following Kant and Friedman, the findings suggest that what simulations capture finite, quantized observations cannot instantiate the ideal properties of an unbounded, dense continuum. Such properties belong to constructive intuition rather than to finite sampling alone. A complementary visualization contrasts the empirical histogram with a sine-curve proxy to clarify this divide. The contribution is interpretive rather than data-expansive: it reframes an existing simulation as a probe of the synthetic a priori structure underlying students' perceptions, showing how formal order-theoretic coherence coexists with principled failures of endpoint-freeness and density in finite empirical models.

Effective communication is essential for safety and efficiency in human-robot collaboration, particularly in shared workspaces. This paper investigates the impact of nonverbal communication on human-robot interaction (HRI) by integrating reactive light signals and emotional displays into a robotic system. We equipped a Franka Emika Panda robot with an LED strip on its end effector and an animated facial display on a tablet to convey movement intent through colour-coded signals and facial expressions. We conducted a human-robot collaboration experiment with 18 participants, evaluating three conditions: LED signals alone, LED signals with reactive emotional displays, and LED signals with pre-emptive emotional displays. We collected data through questionnaires and position tracking to assess anticipation of potential collisions, perceived clarity of communication, and task performance. The results indicate that while emotional displays increased the perceived interactivity of the robot, they did not significantly improve collision anticipation, communication clarity, or task efficiency compared to LED signals alone. These findings suggest that while emotional cues can enhance user engagement, their impact on task performance in shared workspaces is limited.