We consider the problem of estimating how well a model class is capable of fitting a distribution of labeled data. We show that it is often possible to accurately estimate this ``learnability'' even when given an amount of data that is too small to reliably learn any accurate model. Our first result applies to the setting where the data is drawn from a $d$-dimensional distribution with isotropic covariance, and the label of each datapoint is an arbitrary noisy function of the datapoint. In this setting, we show that with $O(\sqrt{d})$ samples, one can accurately estimate the fraction of the variance of the label that can be explained via the best linear function of the data. We extend these techniques to a binary classification, and show that the prediction error of the best linear classifier can be accurately estimated given $O(\sqrt{d})$ labeled samples. For comparison, in both the linear regression and binary classification settings, even if there is no noise in the labels, a sample size linear in the dimension, $d$, is required to \emph{learn} any function correlated with the underlying model. We further extend our estimation approach to the setting where the data distribution has an (unknown) arbitrary covariance matrix, allowing these techniques to be applied to settings where the model class consists of a linear function applied to a nonlinear embedding of the data. We demonstrate the practical viability of our approaches on synthetic and real data. This ability to estimate the explanatory value of a set of features (or dataset), even in the regime in which there is too little data to realize that explanatory value, may be relevant to the scientific and industrial settings for which data collection is expensive and there are many potentially relevant feature sets that could be collected.

We consider the problem of estimating how well a model class is capable of fitting a distribution of labeled data. We show that it is often possible to accurately estimate this ``learnability'' even when given an amount of data that is too small to reliably learn any accurate model. Our first result applies to the setting where the data is drawn from a $d$-dimensional distribution with isotropic covariance, and the label of each datapoint is an arbitrary noisy function of the datapoint. In this setting, we show that with $O(\sqrt{d})$ samples, one can accurately estimate the fraction of the variance of the label that can be explained via the best linear function of the data. We extend these techniques to a binary classification, and show that the prediction error of the best linear classifier can be accurately estimated given $O(\sqrt{d})$ labeled samples. For comparison, in both the linear regression and binary classification settings, even if there is no noise in the labels, a sample size linear in the dimension, $d$, is required to \emph{learn} any function correlated with the underlying model. We further extend our estimation approach to the setting where the data distribution has an (unknown) arbitrary covariance matrix, allowing these techniques to be applied to settings where the model class consists of a linear function applied to a nonlinear embedding of the data. We demonstrate the practical viability of our approaches on synthetic and real data. This ability to estimate the explanatory value of a set of features (or dataset), even in the regime in which there is too little data to realize that explanatory value, may be relevant to the scientific and industrial settings for which data collection is expensive and there are many potentially relevant feature sets that could be collected.

Agentic pipelines present novel challenges and opportunities for human-centered explainability. The HCXAI community is still grappling with how best to make the inner workings of LLMs transparent in actionable ways. Agentic pipelines consist of multiple LLMs working in cooperation with minimal human control. In this research paper, we present early findings from an agentic pipeline implementation of a perceptive task guidance system. Through quantitative and qualitative analysis, we analyze how Chain-of-Thought (CoT) reasoning, a common vehicle for explainability in LLMs, operates within agentic pipelines. We demonstrate that CoT reasoning alone does not lead to better outputs, nor does it offer explainability, as it tends to produce explanations without explainability, in that they do not improve the ability of end users to better understand systems or achieve their goals.

Before explaining what I mean, let me set the scene. Broadly, NLP can be pursued in three mutually overlapping ways, which emphasize different aspects of our work. First, there is NLP as Engineering, where NLP models are built primarily to serve some practical goal, answering a need that exists in society. Second, there is what might be called NLP-as-Mathematics, which studies algorithms and models in their own right, comparing them and developing new ones. Finally, there is NLP-as-Science, where models are constructed with the aim of expressing, testing, and ultimately enhancing humankind's grasp of human language and language use, because computational models offer a level of explicitness and detail that other theories of language often lack.

In this post, I'll take a look at how you can compare regression models. Comparing regression models is perhaps one of the trickiest tasks to complete in the "comparing models" arena; The reason is that there are literally dozens of statistics you can calculate to compare regression models, including: This list isn't exhaustive–there are many other tools, tests and plots at your disposal. Rather than discuss the statistics in detail, I chose to focus this post on comparing a few of the most popular regression model evaluation techniques and discuss when you might want to use them (or when you might not want to). The techniques listed below tend to be on the "easier to use and understand" end of the spectrum, so if you're new to model comparison it's a good place to start. The first question you should be asking is: How well do I know my data?

Recent work in cognitive science has uncovered a diversity of explanatory values, or dimensions along which we judge explanations as better or worse. We propose a Bayesian account of how these values fit together to guide explanation. The resulting taxonomy provides a set of predictors for which explanations people prefer and shows how core values from psychology, statistics, and the philosophy of science emerge from a common mathematical framework. In addition to operationalizing the explanatory virtues associated with, for example, scientific argument-making, this framework also enables us to reinterpret the explanatory vices that drive conspiracy theories, delusions, and extremist ideologies. Intuitively, philosophically, and as seen in laboratory experiments, explanations are judged as better or worse on the basis of many different criteria. These explanatory values appear in early childhood [1, 2, 3, 4, 5] and their influence extends to some of the most sophisticated social knowledge formation processes we know [6]. We lack, however, an understanding of the origin of these values or an account of how they fit together to guide belief formation. The multiplicity of values also appears to conflict with Bayesian models of cognition, which speak solely in terms of degrees of beliefs and suggest we judge explanations as better or worse on the basis of a single quantity, the posterior likelihood (see Glossary). In this opinion, we show how to resolve these conflicts by arguing that previously-identified explanatory values capture different components of a full Bayesian calculation and, when considered together and weighed appropriately, implement Bayesian cognition. This framework shows how key explanatory values identified by laboratory experiments and philosophers of science--co-explanation, descriptiveness, precision, unification, power, and simplicity--emerge naturally from the mathematical structure of probabilistic inference, thereby reconciling them with Bayesian models of cognition [7, 8]. Second, it shows how these values combine to produce preferences for one explanation over another.

We consider the problem of estimating how well a model class is capable of fitting a distribution of labeled data. We show that it is often possible to accurately estimate this learnability'' even when given an amount of data that is too small to reliably learn any accurate model. Our first result applies to the setting where the data is drawn from a $d$-dimensional distribution with isotropic covariance, and the label of each datapoint is an arbitrary noisy function of the datapoint. In this setting, we show that with $O(\sqrt{d})$ samples, one can accurately estimate the fraction of the variance of the label that can be explained via the best linear function of the data. We extend these techniques to a binary classification, and show that the prediction error of the best linear classifier can be accurately estimated given $O(\sqrt{d})$ labeled samples.

In this post, I'll take a look at how you can compare regression models. Comparing regression models is perhaps one of the trickiest tasks to complete in the "comparing models" arena; The reason is that there are literally dozens of statistics you can calculate to compare regression models, including: This list isn't exhaustive--there are many other tools, tests and plots at your disposal. Rather than discuss the statistics in detail, I chose to focus this post on comparing a few of the most popular regression model evaluation techniques and discuss when you might want to use them (or when you might not want to). The techniques listed below tend to be on the "easier to use and understand" end of the spectrum, so if you're new to model comparison it's a good place to start. The first question you should be asking is: How well do I know my data?