arXiv subjects

Hanti Lin

Publications and source records attributed to Hanti Lin.

13 recordsLinked to original sources

arXiv2026

Pessimistic Meta-Induction and Its Limits: Lessons from Frequentist Statistics and Machine Learning Theory

This paper challenges the pessimistic meta-inductive argument against scientific realism by undermining its inductive step rather than its historical premise. Although related challenges already exist, I develop a new one. Drawing on a general epistemology of scientific inference developed in frequentist statistics, machine learning, and formal epistemology, I evaluate induction in terms of convergence to the truth. I argue that ordinary enumerative induction can achieve everywhere convergence, whereas meta-induction fails even to achieve almost everywhere convergence. Indeed, in the problem context where meta-induction arises, the failure is deeper: no inference method whatsoever achieves almost everywhere convergence.

cs.LG↗

arXiv2026

Cross-Entropy Risk Estimation for Language Models: Inconsistency Must Be Dense, and the Holdout Method Is No Exception

Language models are compared by their held-out per-token cross-entropy risk---the quantity scaling laws are fitted to. We show that it cannot be consistently estimated. Consistency, or convergence to the estimand, is defined relative to a \emph{possible state of the world}: a pair consisting of a data-generating distribution and a model we turn out to train. Quantifying over models as well as data-generating mechanisms is essential, because what decides whether a model's risk is estimable is a tail property of the distribution its weights induce, which no sample reveals. The per-token cross-entropy risk is hard to estimate because of a topological fact: among the possible states, finite risk and infinite risk each lie arbitrarily close to every instance of the other. Consequently no estimator---not merely the holdout average---is consistent at every state at which the risk is defined. Worse, inconsistent estimation persists under both bounding the expected sequence length and restricting to full-support models; and in that restricted setting the states at which inconsistency occurs are even dense. Two interesting ways out are identified, and neither is free. Way out 1: using a bounded context window, we can floor a model's next-token probabilities, making its risk finite exactly when the data-generating distribution has finite expected sequence length---a new, statistical rationale for a choice that was made on computational grounds, though the assumption it substitutes is itself beyond the reach of any test. Way out 2: reporting the risk only when it falls below a threshold fixed in advance restores consistency, at no cost to what model selection actually requires---but we need to recognize that the goal of estimation is revised.

cs.LG↗

arXiv2026

Meager Success: A Theory of the Unlearnable for Hypothesis Testing

When the standard of pointwise consistency for statistical inference -- convergence to the truth in every possible state of the world -- is provably unachievable, the usual responses are to change the inferential target or to strengthen background assumptions. This paper pursues a third: hold the inference problem fixed and identify the highest standard that remains achievable. I define a hierarchy of standards weaker than pointwise consistency, cast in topological terms, requiring convergence to the truth not everywhere but on a ``large'' set of probability measures. The main result is an impossibility theorem: for finite-precision tests, converging to the truth densely within each hypothesis already forces inconsistency on a comeager -- ``topologically almost all'' -- set of measures, whenever the two hypotheses are dense in their union. Distribution-free testing of conditional independence is one such case. Two further theorems characterize, in purely topological terms, exactly when each weaker standard is achievable, complementing Boeken et al.'s (2026) analysis of pointwise consistency.

math.ST↗

arXiv2026

Never Too LATE: A Fully Stochastic Update to the Potential Outcome Framework

In the classic potential outcome framework, the local average treatment effect (LATE) and its identification via an instrumental variable are stated in a deterministic setting at the individual level: each individual has settled potential outcomes such as ``cured if treated''. Several authors have proposed working instead with \emph{stochastic} potential outcomes -- counterfactual probabilities of the form ``the chance of being cured if treated'' -- but the integration of stochastic potential outcomes with the LATE machinery raises an issue. It is a metaphysical issue: in a stochastic setting, the standard joint-probability definitions of compliers and the LATE assume what I will call the \emph{unique-parallel-universe view}, which asserts that, in any genuinely possible state of the world, every counterfactual condition settles a unique determinate outcome even when the underlying causal disposition is irreducibly chancy. The statistician Dawid (2000) doubts the plausibility of this view; the philosopher Lewis (1973) develops a reductio argument against it. I propose a fully stochastic update to the Rubin causal model that drops the assumption of the unique-parallel-universe view: stochastic potential outcomes are introduced as Bernoulli parameters in their own (small) probability spaces, and are connected to observables via the factorization rule of a causal Bayes net. Within this framework, I define a Degree-of-compliance-weighted Average Treatment Effect (DATE) and prove that, under assumptions analogous to those used for the LATE but rewritten for the fully stochastic setting, the DATE equals the usual IV estimand. The classic LATE identification result emerges as a deterministic special case. Existing IV practice can therefore be reinterpreted: it has been estimating the DATE all along, in a general stochastic setting, without assuming the unique-parallel-universe view.

stat.ME↗

arXiv2025

A Plea for History and Philosophy of Statistics and Machine Learning

The integration of the history and philosophy of statistics was initiated at least by Hacking (1975) and advanced by Hacking (1990), Mayo (1996), and Zabell (2005), but it has not received sustained follow-up. Yet such integration is more urgent than ever, as the recent success of artificial intelligence has been driven largely by machine learning -- a field historically developed alongside statistics. Today, the boundary between statistics and machine learning is increasingly blurred. What we now need is integration, twice over: of history and philosophy, and of two fields they engage -- statistics and machine learning. I present a case study of a philosophical idea in machine learning (and in formal epistemology) whose root can be traced back to an often under-appreciated insight in Neyman and Pearson's 1936 work (a follow-up to their 1933 classic). This leads to the articulation of an epistemological principle -- largely implicit in, but shared by, the practices of frequentist statistics and machine learning -- which I call achievabilism: the thesis that the correct standard for assessing non-deductive inference methods should not be fixed, but should instead be sensitive to what is achievable in specific problem contexts. Another integration also emerges at the level of methodology, combining two ends of the philosophy of science spectrum: history and philosophy of science on the one hand, and formal epistemology on the other hand.

stat.OT↗

arXiv2025

The Problem of the Priors, or Posteriors?

The problem of the priors is well known: it concerns the challenge of identifying norms that govern one's prior credences. I argue that a key to addressing this problem lies in considering what I call the problem of the posteriors -- the challenge of identifying norms that directly govern one's posterior credences, which backward induce some norms on the priors via the diachronic requirement of conditionalization. This forward-looking approach can be summarized as: Think ahead, work backward. Although this idea can be traced to Freedman (1963), Carnap (1963), and Shimony (1970), I believe that it has not received enough attention. In this paper, I initiate a systematic defense of forward-looking Bayesianism, addressing potential objections from more traditional views (both subjectivist and objectivist). I also develop a specific approach to forward-looking Bayesianism -- one that values the convergence of posterior credences to the truth, and treats it as a fundamental rather than derived norm. This approach, called convergentist Bayesianism, is argued to be crucial for a Bayesian foundation of Ockham's razor in statistics and machine learning.

stat.OT↗

arXiv2024

Scientific Realism vs. Anti-Realism: Toward a Common Ground

The debate between scientific realism and anti-realism remains at a stalemate, making reconciliation seem hopeless. Yet, important work remains: exploring a common ground, even if only to uncover deeper points of disagreement and, ideally, to benefit both sides of the debate. I propose such a common ground. Specifically, many anti-realists, such as instrumentalists, have yet to seriously engage with Sober's call to justify their preferred version of Ockham's razor through a positive account. Meanwhile, realists face a similar challenge: providing a non-circular explanation of how their version of Ockham's razor connects to truth. The common ground I propose addresses these challenges for both sides; the key is to leverage the idea that everyone values some truths and to draw on insights from scientific fields that study scientific inference -- namely, statistics and machine learning. This common ground also isolates a distinctively epistemic root of the irreconcilability in the realism debate.

stat.OT↗

arXiv2024

Unified Inductive Logic: From Formal Learning to Statistical Inference to Supervised Learning

While the traditional conception of inductive logic is Carnapian, I develop a Peircean alternative and use it to unify formal learning theory, statistics, and a significant part of machine learning: supervised learning. Some crucial standards for evaluating non-deductive inferences have been assumed separately in those areas, but can actually be justified by a unifying principle.

stat.OT↗

arXiv2024

Internalist Reliabilism in Statistics and Machine Learning: Thoughts on Jun Otsuka's Thinking about Statistics

Otsuka (2023) argues for a correspondence between data science and traditional epistemology: Bayesian statistics is internalist; classical (frequentist) statistics is externalist, owing to its reliabilist nature; model selection is pragmatist; and machine learning is a version of virtue epistemology. Where he sees diversity, I see an opportunity for unity. In this article, I argue that classical statistics, model selection, and machine learning share a foundation that is reliabilist in an unconventional sense that aligns with internalism. Hence a unification under internalist reliabilism.

stat.OT↗

arXiv2024

Frequentist Statistics as Internalist Reliabilism

There has long been an impression that reliabilism implies externalism and that frequentist statistics, due to its reliabilist nature, is inherently externalist. I argue, however, that frequentist statistics can plausibly be understood as a form of internalist reliabilism -- internalist in the conventional sense, yet reliabilist in certain unconventional and intriguing ways. Crucially, in developing the thesis that reliabilism does not imply externalism, my aim is not to stretch the meaning of `reliabilism' merely to sever the implication. Instead, it is to gain a deeper understanding of frequentist statistics, which stands as one of the most sustained attempts by scientists to develop an epistemology for their own use.

stat.OT↗

arXiv2024

Convergence to the Truth

This article reviews and develops an epistemological tradition in the philosophy of science, known as convergentism, which holds that inference methods should be assessed based on their ability to converge to the truth across a range of possible scenarios. Emphasis is placed on its historical origins in the work of C. S. Peirce and its recent developments in formal epistemology and data science (including statistics and machine learning). Comparisons are made with three other traditions: (1) explanationism, which holds that theory choice should be guided by a theory's overall balance of explanatory virtues, such as simplicity and fit with data; (2) instrumentalism, which maintains that scientific inference should be driven by the goal of obtaining useful models rather than true theories; and (3) Bayesianism, which shifts the focus from all-or-nothing beliefs to degrees of belief.

stat.OT↗

arXiv2024

The Logic of Counterfactuals and the Epistemology of Causal Inference

The 2021 Nobel Prize in Economics recognized an epistemology of causal inference based on the Rubin causal model (Rubin 1974), which merits broader attention in philosophy. This model, in fact, presupposes a logical principle of counterfactuals, Conditional Excluded Middle (CEM), the locus of a pivotal debate between Stalnaker (1968) and Lewis (1973) on the semantics of counterfactuals. Proponents of CEM should recognize that this connection points to a new argument for CEM -- a Quine-Putnam indispensability argument grounded in the Nobel-winning applications of the Rubin model in health and social sciences. To advance the dialectic, I challenge this argument with an updated Rubin causal model that retains its successes while dispensing with CEM. This novel approach combines the strengths of the Rubin causal model and a causal model familiar in philosophy, the causal Bayes net. The takeaway: deductive logic and inductive inference, often studied in isolation, are deeply interconnected.

cs.AI↗

arXiv2018

On Learning Causal Structures from Non-Experimental Data without Any Faithfulness Assumption

Consider the problem of learning, from non-experimental data, the causal (Markov equivalence) structure of the true, unknown causal Bayesian network (CBN) on a given, fixed set of (categorical) variables. This learning problem is known to be so hard that there is no learning algorithm that converges to the truth for all possible CBNs (on the given set of variables). So the convergence property has to be sacrificed for some CBNs---but for which? In response, the standard practice has been to design and employ learning algorithms that secure the convergence property for at least all the CBNs that satisfy the famous faithfulness condition, which implies sacrificing the convergence property for some CBNs that violate the faithfulness condition (Spirtes et al. 2000). This standard design practice can be justified by assuming---that is, accepting on faith---that the true, unknown CBN satisfies the faithfulness condition. But the real question is this: Is it possible to explain, without assuming the faithfulness condition or any of its weaker variants, why it is mandatory rather than optional to follow the standard design practice? This paper aims to answer the above question in the affirmative. We first define an array of modes of convergence to the truth as desiderata that might or might not be achieved by a causal learning algorithm. Those modes of convergence concern (i) how pervasive the domain of convergence is on the space of all possible CBNs and (ii) how uniformly the convergence happens. Then we prove a result to the following effect: for any learning algorithm that tackles the causal learning problem in question, if it achieves the best achievable mode of convergence (considered in this paper), then it must follow the standard design practice of converging to the truth for at least all CBNs that satisfy the faithfulness condition---it is a requirement, not an option.

stat.ML↗