Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2009.14148

Unbalanced Sobolev Descent

Youssef Mroueh·Mattia Rigotti
View original source ↗Read source document ↗Export metadata ↓

Abstract

We introduce Unbalanced Sobolev Descent (USD), a particle descent algorithm for transporting a high dimensional source distribution to a target distribution that does not necessarily have the same mass. We define the Sobolev-Fisher discrepancy between distributions and show that it relates to advection-reaction transport equations and the Wasserstein-Fisher-Rao metric between distributions. USD transports particles along gradient flows of the witness function of the Sobolev-Fisher discrepancy (advection step) and reweighs the mass of particles with respect to this witness function (reaction step). The reaction step can be thought of as a birth-death process of the particles with rate of growth proportional to the witness function. When the Sobolev-Fisher witness function is estimated in a Reproducing Kernel Hilbert Space (RKHS), under mild assumptions we show that USD converges asymptotically (in the limit of infinite particles) to the target distribution in the Maximum Mean Discrepancy (MMD) sense. We then give two methods to estimate the Sobolev-Fisher witness with neural networks, resulting in two Neural USD algorithms. The first one implements the reaction step with mirror descent on the weights, while the second implements it through a birth-death process of particles. We show on synthetic examples that USD transports distributions with or without conservation of mass faster than previous particle descent algorithms, and finally demonstrate its use for molecular biology analyses where our method is naturally suited to match developmental stages of populations of differentiating cells based on their single-cell RNA sequencing profile. Code is available at https://github.com/ibm/usd .

Explore related subjects

cs.LGstat.ML

Keep this discovery

BibTeXRIS

Youssef Mroueh, Mattia Rigotti. 2020-09-29. Unbalanced Sobolev Descent. https://arxiv.org/abs/2009.14148

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

AUC Maximization from Biased Positive-unlabeled Data with Confidence

Maximizing the area under the receiver operating characteristic curve (AUC) is a standard approach to imbalanced binary classification. Although positive and negative data are required for maximizing the AUC, negative data are often difficult to collect in some real-world applications due to privacy concerns or the need for specialized expertise to annotate them. Thus, AUC maximization from positive and unlabeled (PU) data has been attracting attention. Existing methods assume that labeled positive data are unbiased samples from the true positive distribution. However, this ideal assumption is often violated in practice. In this paper, we propose a method to maximize the AUC from biased PU data. To address the bias, our key idea is to exploit {\it confidence}, i.e., the probability that an instance is positive, associated with the small number of labeled positive data. We derive an estimator of the AUC risk using biased PU data with confidence, enabling AUC maximization under such bias. We further show that the rewritten AUC risk induces a Bayes-optimal AUC ranking even when the available confidence is any strictly increasing transformation of the true posterior probability. We experimentally show the effectiveness of our method on eight real-world datasets.

cs.LG↗
arXiv2026

Measuring the Value of World-Model Updates: A Counterfactual Utility Protocol for Continual Adaptation

Continual world models must decide whether new data justify changing the model. Fixed replay schedules and prediction-error triggers specify when to update, but neither reveals the value of an individual update: one deployment run cannot show how the same model would have performed at that moment had it held its parameters. We introduce the fork ledger, which branches a deployment stream at pre-registered decision points into matched update and hold continuations under common random numbers. It evaluates both continuations on the same episodes and records $\Delta R = R_{\mathrm{update}} - R_{\mathrm{hold}}$. Always applying one fixed update mechanism lowers return on all three simulated control tasks: CartPole ($-144.0$; checkpoint-bootstrap $95\%$ CI $[-185.4,-116.1]$, against a converged return near $650$), Walker ($-82.8$; $[-101.1,-61.7]$) and Cheetah ($-18.6$; $[-29.0,-6.6]$). Divergence is an outcome of applying the update, so the estimand counts every attempted fork; restricted to the $693$ of $720$ that did not collapse, CartPole and Walker are unchanged in sign ($-113.4$ and $-82.1$) and Cheetah becomes unresolved ($-3.9$; $[-17.5,+13.0]$). The task is the unit of inference: each contributes $240$ attempted forks over five pretrained checkpoints crossed with two drift directions. The ledger makes counterfactual utility observable for a fixed mechanism, allowing triggers to be judged by the updates they select rather than by surprise detection alone.

cs.LG↗
arXiv2026

When More Is Not Better: Component Anti-Synergy in a P300 Speller

P300 brain-computer interface (BCI) spellers can provide hands-free communication for people with severe motor impairments. Modern pipelines combine multiple individually promising components, often assuming that 'more-is-better'. We tested this assumption using a four-component full-factorial experiment varying the inclusion of Euclidean Alignment (EA), xDAWN spatial filtering, subject calibration, and language model priors on a public P300 dataset. Performance was evaluated using accuracy, repetitions, and information transfer rate (ITR) with mixed-effects models. Results show that the value of components is conditional rather than additive. Calibration was the strongest singular contributor, while EA compensated for its absence in zero-calibration settings. Adding independently useful components could also reduce performance, revealing component anti-synergy. Contrary to conventional wisdom, LM support was not universally beneficial: its effect depends strongly on the strength of the underlying EEG pipeline, while results from a larger LM showed a similar pattern. Together, these findings challenge maximal 'all-on' pipeline design and highlight the value of selecting spatial and language-support components according to the quality of available EEG evidence.

cs.LG↗