arXiv subjects

Richard Nock

Publications and source records attributed to Richard Nock.

At least 19 recordsLinked to original sources

arXiv2026

Density-Ratio Losses for Post-Hoc Learning to Defer

We study post-hoc Learning to Defer (L2D) through the lens of ideal distributions: divergence-regularized reweightings of the data distribution under which a model attains low loss. We define deferral via the density-ratio between a model's and an expert's ideals. Using the reduction from density-ratio estimation to class-probability estimation, we derive the DR CPE losses for post-hoc L2D scorers. Deferral decisions are then made by thresholding the scorer, allowing deferral rates to be adjusted without retraining. For KL-based ideal distributions, our deferral rules recovers Chow's rule under the original distribution and a connection to an expert-tilted Bayes posterior -- which incorporates the expert's performance -- depending on if the ideal distributions are joint or marginal distributions. Experimentally, our approach is competitive compared to common baselines and more robust across dataset settings. More broadly, our results cast post-hoc L2D as density-ratio learning between ideal distributions, bridging Chow-style rules, expert comparison, and elucidating connections to related learning settings including anomaly detection.

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arXiv2026

Seasoning Generative Models for a Generalization Aftertaste

The use of discriminators to train or fine-tune generative models has proven to be a rather successful framework. A notable example is Generative Adversarial Networks (GANs) that minimize a loss incurred by training discriminators along with other paradigms that boost generative models via discriminators that satisfy weak learner constraints. More recently, even diffusion models have shown advantages with some kind of discriminator guidance. In this work, we extend a strong-duality result related to $f$-divergences which gives rise to a discriminator-guided recipe that allows us to \textit{refine} any generative model. We then show that the refined generative models provably improve generalization, compared to its non-refined counterpart. In particular, our analysis reveals that the gap in generalization is improved based on the Rademacher complexity of the discriminator set used for refinement. Our recipe subsumes a recently introduced score-based diffusion approach (Kim et al., 2022) that has shown great empirical success, however allows us to shed light on the generalization guarantees of this method by virtue of our analysis. Thus, our work provides a theoretical validation for existing work, suggests avenues for new algorithms, and contributes to our understanding of generalization in generative models at large.

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arXiv2025

DPO Unchained: Your Training Algorithm is Secretly Disentangled in Human Choice Theory (and its Loss' Convexity is Dispensable)

Normative theories allow one to elicit key parts of a ML algorithm from first principles, which is crucial at a time of championed scrutiny for ML work. Direct Preference Optimization (DPO) cleverly bypasses reward modeling by making an explicit link with a specific normative model of human choice. Our paper elevates this connection to the full generality of DPO's normative framework. Getting there requires reworking human choice theory's textbook path for a better RLHF/ML fit. It elevates the connection to a remarkably broad viewpoint on preference optimization, considering the current panorama of DPO follow-ups. It also unveils unexpected riches for ML, chief among which the support for non-convex losses, the fact that any compliant ML analytical choice can be embedded with any human choice model, and a normative framework's umbrella wide enough to safeguard DPO's extensions (margins, length correction, ...). A toy experiment ``far away'' from the DPO crowd is given.

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arXiv2024

How to Boost Any Loss Function

Boosting is a highly successful ML-born optimization setting in which one is required to computationally efficiently learn arbitrarily good models based on the access to a weak learner oracle, providing classifiers performing at least slightly differently from random guessing. A key difference with gradient-based optimization is that boosting's original model does not requires access to first order information about a loss, yet the decades long history of boosting has quickly evolved it into a first order optimization setting -- sometimes even wrongfully defining it as such. Owing to recent progress extending gradient-based optimization to use only a loss' zeroth ($0^{th}$) order information to learn, this begs the question: what loss functions can be efficiently optimized with boosting and what is the information really needed for boosting to meet the original boosting blueprint's requirements? We provide a constructive formal answer essentially showing that any loss function can be optimized with boosting and thus boosting can achieve a feat not yet known to be possible in the classical $0^{th}$ order setting, since loss functions are not required to be be convex, nor differentiable or Lipschitz -- and in fact not required to be continuous either. Some tools we use are rooted in quantum calculus, the mathematical field -- not to be confounded with quantum computation -- that studies calculus without passing to the limit, and thus without using first order information.

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arXiv2024

Label Noise Robustness for Domain-Agnostic Fair Corrections via Nearest Neighbors Label Spreading

Last-layer retraining methods have emerged as an efficient framework for correcting existing base models. Within this framework, several methods have been proposed to deal with correcting models for subgroup fairness with and without group membership information. Importantly, prior work has demonstrated that many methods are susceptible to noisy labels. To this end, we propose a drop-in correction for label noise in last-layer retraining, and demonstrate that it achieves state-of-the-art worst-group accuracy for a broad range of symmetric label noise and across a wide variety of datasets exhibiting spurious correlations. Our proposed approach uses label spreading on a latent nearest neighbors graph and has minimal computational overhead compared to existing methods.

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arXiv2024

Boosting gets full Attention for Relational Learning

More often than not in benchmark supervised ML, tabular data is flat, i.e. consists of a single $m \times d$ (rows, columns) file, but cases abound in the real world where observations are described by a set of tables with structural relationships. Neural nets-based deep models are a classical fit to incorporate general topological dependence among description features (pixels, words, etc.), but their suboptimality to tree-based models on tabular data is still well documented. In this paper, we introduce an attention mechanism for structured data that blends well with tree-based models in the training context of (gradient) boosting. Each aggregated model is a tree whose training involves two steps: first, simple tabular models are learned descending tables in a top-down fashion with boosting's class residuals on tables' features. Second, what has been learned progresses back bottom-up via attention and aggregation mechanisms, progressively crafting new features that complete at the end the set of observation features over which a single tree is learned, boosting's iteration clock is incremented and new class residuals are computed. Experiments on simulated and real-world domains display the competitiveness of our method against a state of the art containing both tree-based and neural nets-based models.

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arXiv2024

Robustness to Subpopulation Shift with Domain Label Noise via Regularized Annotation of Domains

Existing methods for last layer retraining that aim to optimize worst-group accuracy (WGA) rely heavily on well-annotated groups in the training data. We show, both in theory and practice, that annotation-based data augmentations using either downsampling or upweighting for WGA are susceptible to domain annotation noise, and in high-noise regimes approach the WGA of a model trained with vanilla empirical risk minimization. We introduce Regularized Annotation of Domains (RAD) in order to train robust last layer classifiers without the need for explicit domain annotations. Our results show that RAD is competitive with other recently proposed domain annotation-free techniques. Most importantly, RAD outperforms state-of-the-art annotation-reliant methods even with only 5% noise in the training data for several publicly available datasets.

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arXiv2024

Tempered Calculus for ML: Application to Hyperbolic Model Embedding

Most mathematical distortions used in ML are fundamentally integral in nature: $f$-divergences, Bregman divergences, (regularized) optimal transport distances, integral probability metrics, geodesic distances, etc. In this paper, we unveil a grounded theory and tools which can help improve these distortions to better cope with ML requirements. We start with a generalization of Riemann integration that also encapsulates functions that are not strictly additive but are, more generally, $t$-additive, as in nonextensive statistical mechanics. Notably, this recovers Volterra's product integral as a special case. We then generalize the Fundamental Theorem of calculus using an extension of the (Euclidean) derivative. This, along with a series of more specific Theorems, serves as a basis for results showing how one can specifically design, alter, or change fundamental properties of distortion measures in a simple way, with a special emphasis on geometric- and ML-related properties that are the metricity, hyperbolicity, and encoding. We show how to apply it to a problem that has recently gained traction in ML: hyperbolic embeddings with a "cheap" and accurate encoding along the hyperbolic vs Euclidean scale. We unveil a new application for which the Poincar\'e disk model has very appealing features, and our theory comes in handy: \textit{model} embeddings for boosted combinations of decision trees, trained using the log-loss (trees) and logistic loss (combinations).

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arXiv2023

The Tempered Hilbert Simplex Distance and Its Application To Non-linear Embeddings of TEMs

Tempered Exponential Measures (TEMs) are a parametric generalization of the exponential family of distributions maximizing the tempered entropy function among positive measures subject to a probability normalization of their power densities. Calculus on TEMs relies on a deformed algebra of arithmetic operators induced by the deformed logarithms used to define the tempered entropy. In this work, we introduce three different parameterizations of finite discrete TEMs via Legendre functions of the negative tempered entropy function. In particular, we establish an isometry between such parameterizations in terms of a generalization of the Hilbert log cross-ratio simplex distance to a tempered Hilbert co-simplex distance. Similar to the Hilbert geometry, the tempered Hilbert distance is characterized as a $t$-symmetrization of the oriented tempered Funk distance. We motivate our construction by introducing the notion of $t$-lengths of smooth curves in a tautological Finsler manifold. We then demonstrate the properties of our generalized structure in different settings and numerically examine the quality of its differentiable approximations for optimization in machine learning settings.

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arXiv2023

Optimal Transport with Tempered Exponential Measures

In the field of optimal transport, two prominent subfields face each other: (i) unregularized optimal transport, "\`a-la-Kantorovich", which leads to extremely sparse plans but with algorithms that scale poorly, and (ii) entropic-regularized optimal transport, "\`a-la-Sinkhorn-Cuturi", which gets near-linear approximation algorithms but leads to maximally un-sparse plans. In this paper, we show that an extension of the latter to tempered exponential measures, a generalization of exponential families with indirect measure normalization, gets to a very convenient middle ground, with both very fast approximation algorithms and sparsity, which is under control up to sparsity patterns. In addition, our formulation fits naturally in the unbalanced optimal transport problem setting.

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arXiv2023

Generative Forests

We focus on generative AI for a type of data that still represent one of the most prevalent form of data: tabular data. Our paper introduces two key contributions: a new powerful class of forest-based models fit for such tasks and a simple training algorithm with strong convergence guarantees in a boosting model that parallels that of the original weak / strong supervised learning setting. This algorithm can be implemented by a few tweaks to the most popular induction scheme for decision tree induction (i.e. supervised learning) with two classes. Experiments on the quality of generated data display substantial improvements compared to the state of the art. The losses our algorithm minimize and the structure of our models make them practical for related tasks that require fast estimation of a density given a generative model and an observation (even partially specified): such tasks include missing data imputation and density estimation. Additional experiments on these tasks reveal that our models can be notably good contenders to diverse state of the art methods, relying on models as diverse as (or mixing elements of) trees, neural nets, kernels or graphical models.

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arXiv2023

Boosting with Tempered Exponential Measures

One of the most popular ML algorithms, AdaBoost, can be derived from the dual of a relative entropy minimization problem subject to the fact that the positive weights on the examples sum to one. Essentially, harder examples receive higher probabilities. We generalize this setup to the recently introduced {\it tempered exponential measure}s (TEMs) where normalization is enforced on a specific power of the measure and not the measure itself. TEMs are indexed by a parameter $t$ and generalize exponential families ($t=1$). Our algorithm, $t$-AdaBoost, recovers AdaBoost~as a special case ($t=1$). We show that $t$-AdaBoost retains AdaBoost's celebrated exponential convergence rate when $t\in [0,1)$ while allowing a slight improvement of the rate's hidden constant compared to $t=1$. $t$-AdaBoost partially computes on a generalization of classical arithmetic over the reals and brings notable properties like guaranteed bounded leveraging coefficients for $t\in [0,1)$. From the loss that $t$-AdaBoost minimizes (a generalization of the exponential loss), we show how to derive a new family of {\it tempered} losses for the induction of domain-partitioning classifiers like decision trees. Crucially, strict properness is ensured for all while their boosting rates span the full known spectrum. Experiments using $t$-AdaBoost+trees display that significant leverage can be achieved by tuning $t$.

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arXiv2023

Smoothly Giving up: Robustness for Simple Models

There is a growing need for models that are interpretable and have reduced energy and computational cost (e.g., in health care analytics and federated learning). Examples of algorithms to train such models include logistic regression and boosting. However, one challenge facing these algorithms is that they provably suffer from label noise; this has been attributed to the joint interaction between oft-used convex loss functions and simpler hypothesis classes, resulting in too much emphasis being placed on outliers. In this work, we use the margin-based $α$-loss, which continuously tunes between canonical convex and quasi-convex losses, to robustly train simple models. We show that the $α$ hyperparameter smoothly introduces non-convexity and offers the benefit of "giving up" on noisy training examples. We also provide results on the Long-Servedio dataset for boosting and a COVID-19 survey dataset for logistic regression, highlighting the efficacy of our approach across multiple relevant domains.

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arXiv2023

LegendreTron: Uprising Proper Multiclass Loss Learning

Loss functions serve as the foundation of supervised learning and are often chosen prior to model development. To avoid potentially ad hoc choices of losses, statistical decision theory describes a desirable property for losses known as \emph{properness}, which asserts that Bayes' rule is optimal. Recent works have sought to \emph{learn losses} and models jointly. Existing methods do this by fitting an inverse canonical link function which monotonically maps $\mathbb{R}$ to $[0,1]$ to estimate probabilities for binary problems. In this paper, we extend monotonicity to maps between $\mathbb{R}^{C-1}$ and the projected probability simplex $\tilde{\Delta}^{C-1}$ by using monotonicity of gradients of convex functions. We present {\sc LegendreTron} as a novel and practical method that jointly learns \emph{proper canonical losses} and probabilities for multiclass problems. Tested on a benchmark of domains with up to 1,000 classes, our experimental results show that our method consistently outperforms the natural multiclass baseline under a $t$-test at 99% significance on all datasets with greater than 10 classes.

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arXiv2022

Clustering above Exponential Families with Tempered Exponential Measures

The link with exponential families has allowed $k$-means clustering to be generalized to a wide variety of data generating distributions in exponential families and clustering distortions among Bregman divergences. Getting the framework to work above exponential families is important to lift roadblocks like the lack of robustness of some population minimizers carved in their axiomatization. Current generalisations of exponential families like $q$-exponential families or even deformed exponential families fail at achieving the goal. In this paper, we provide a new attempt at getting the complete framework, grounded in a new generalisation of exponential families that we introduce, tempered exponential measures (TEM). TEMs keep the maximum entropy axiomatization framework of $q$-exponential families, but instead of normalizing the measure, normalize a dual called a co-distribution. Numerous interesting properties arise for clustering such as improved and controllable robustness for population minimizers, that keep a simple analytic form.

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arXiv2022

Fair Wrapping for Black-box Predictions

We introduce a new family of techniques to post-process ("wrap") a black-box classifier in order to reduce its bias. Our technique builds on the recent analysis of improper loss functions whose optimization can correct any twist in prediction, unfairness being treated as a twist. In the post-processing, we learn a wrapper function which we define as an $α$-tree, which modifies the prediction. We provide two generic boosting algorithms to learn $α$-trees. We show that our modification has appealing properties in terms of composition of $α$-trees, generalization, interpretability, and KL divergence between modified and original predictions. We exemplify the use of our technique in three fairness notions: conditional value-at-risk, equality of opportunity, and statistical parity; and provide experiments on several readily available datasets.

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arXiv2022

Proper-Composite Loss Functions in Arbitrary Dimensions

The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules via the proper-composite representation, in which predictions are mapped to probability distributions which are then scored via a scoring rule. However, recent research so far has primarily been concerned with analysing the (typically) finite-dimensional conditional risk problem on the output space, leaving aside the larger total risk minimisation. We generalise a number of these results to an infinite dimensional setting and in doing so we are able to exploit the familial resemblance of density and conditional density estimation to provide a simple characterisation of the canonical link.

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arXiv2022

What killed the Convex Booster ?

A landmark negative result of Long and Servedio established a worst-case spectacular failure of a supervised learning trio (loss, algorithm, model) otherwise praised for its high precision machinery. Hundreds of papers followed up on the two suspected culprits: the loss (for being convex) and/or the algorithm (for fitting a classical boosting blueprint). Here, we call to the half-century+ founding theory of losses for class probability estimation (properness), an extension of Long and Servedio's results and a new general boosting algorithm to demonstrate that the real culprit in their specific context was in fact the (linear) model class. We advocate for a more general stanpoint on the problem as we argue that the source of the negative result lies in the dark side of a pervasive -- and otherwise prized -- aspect of ML: \textit{parameterisation}.

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