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475 papers
The results indicate that mixtures of M\"obius distributions provide interpretable, parsimonious models for the studied steady state density distributions, that match or outperform the alternatives.
Treatment allocation under budget constraints is a central challenge in digital advertising. The standard approach trains an offline uplift model on historical data, then solves a constrained optimization to allocate budget. This fails in cold-start settings where little historical data exists. We propose Budget-Constrained Causal Bandits (BCCB), an online framework that learns which users respond to ads while simultaneously spending the budget. BCCB unifies three components: learning individual-level treatment effects, exploring users whose response is uncertain, and pacing the budget over time. We derive the per-arrival decision rule as the KKT condition of a Lagrangian relaxation of the budgeted causal-allocation objective, providing a principled foundation for the algorithm. We evaluate on the Criteo Uplift dataset using 20 random seeds with paired statistical tests. Our central finding is a data-efficiency crossover at n = 7,500 historical observations (paired one-sided t-test, p = 0.043): below this threshold, offline pipelines either fail or produce unreliable allocations, while BCCB operates from the first user. BCCB exhibits 2-4x lower run-to-run variance than offline methods and outperforms all four online baselines (Thompson Sampling, budgeted Thompson Sampling, HTE Greedy, and Uplifting Bandits) at every budget level tested (p < 0.001). These results give practitioners a concrete decision rule for choosing between offline and online paradigms.
This work benchmarks several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods (continuous generative flow networks), and proposes a novel exploration strategy for off-policy methods, based on local search in the target space with the use of a replay buffer.
This paper proposes a method to approximate the joint posterior over not only the structure of a Bayesian Network, but also the parameters of its conditional probability distributions, using a single GFlowNet whose sampling policy follows a two-phase process.
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It is proved that any global minimizer of the trajectory balance objective can define a policy that samples exactly from the target distribution, and empirically demonstrate the benefits of the trajectories balance objective for GFlowNet convergence, diversity of generated samples, and robustness to long action sequences and large action spaces.
Together, the results clarify how the input geometry shapes the kernel features and fundamentally impacts its generalization properties and clarify how the input geometry shapes the kernel features and fundamentally impacts its generalization properties.
For finite-dimensional linear inverse problems where the variables are Gaussian, it is well-known that the minimum-mean-square error estimator takes the form of a regularized least-squares data fit. In this chapter, we show that this equivalence extends to a much broader infinite-dimensional setting where generalized splines take the role of linear regressors and generalized Gaussian processes on a nuclear space $S$ are the counterpart of Gaussian random vectors. The scope of this extension is of the same nature as the switch from the classic notion of function to that of a distribution, also known as a"generalized function."Our formalism involves a whitening/regularization operator $L: S\to S'$ whose continuous extension induces a native Hilbert space $H\subset S'$ that plays a central role in our characterization. The presentation is self-contained for the most part and remarkably general and powerful. It allows for the recovery of all known instances of such equivalences; in particular, the methods involving innovations and reproducing-kernel Hilbert spaces developed by Kailath and his students, and the mathematical correspondence between fractional splines and Mandelbrot's fractional Brownian motion (fractals), with the former being the optimal estimators of the latter. It also covers general Bayesian methods for the resolution of infinite-dimensional inverse problems.
Global goodness-of-fit and discrepancy statistics can establish that a sample departs from a reference distribution without identifying which observations drive the departure. We develop a framework for this localization problem by assigning to each observation its conditional or marginal contribution across random statistical contexts. This connects resampling diagnostics and data valuation to projection theory and event-level anomaly detection. For symmetric statistics, fixed-size replacement is exactly equivalent to centered conditional localization. For U-statistics, the addition score equals the first Hoeffding/H\'ajek contribution; for smooth distributional functionals it is related at leading order to the influence function; and for unbiased known-background MMD it reduces exactly to the MMD witness. This viewpoint also yields more efficient estimators. Matched-context subtraction removes fluctuations unrelated to the observation, while for pairwise MMD the event-containing terms give a simple localizer. On the LHC Olympics anomaly-detection benchmark, the pair estimator converges to the direct empirical MMD witness with the predicted 1/(Rm^2) scaling, where m is batch size and R the number of batches. At m=1000 and R=5x106 it reaches correlation 0.9993 with essentially identical AUC. We also ask when context contains information beyond an event's own features. In a shared-latent toy model, the full single-event signal and background distributions are identical by construction, forcing isolated-event AUC=0.5. Discriminating information survives only in cross-event dependence induced by the shared latent parameter; the ensemble recovers this information, whereas an independent-latent control does not. This separates two roles of context: efficient localization of a global discrepancy and genuinely additional class information when the alternative contains shared structure.
We extend the FLOP (fast learning of order and parents) algorithm recently proposed by Wien\"obst et al. (2026) from observational to interventional data. In particular, we use the interventional BIC score of Hauser and B\"uhlmann (2012), adapting it to be used with the iterative Cholesky-based score updates that are partly responsible for FLOP's speed. We show that, in the sample limit, I-FLOP recovers a DAG in the same interventional Markov equivalence class as the data-generating DAG. We compare I-FLOP to existing causal structure learning algorithms on real and simulated interventional data, where it performs favorably in terms of both performance and run time.
It is shown that the MEM dual problem admits a reformulation as an expected risk minimization problem, thereby placing MEM within the modern framework of stochastic optimization and enabling scalable stochastic gradient algorithms for large-scale inverse problems.
A mathematical theory of superposition in neural networks using tools from frame theory and compressed sensing and a novel characterization of the distribution of signs in the Gram matrix is developed.
Network comparison using optimal transport is a growing area of research in network science. Unlike standard graph metrics, optimal transport computes both network dissimilarity and a transport plan that explains how one graph morphs into another. In this paper, we review how optimal transport compares undirected, unweighted graphs using three primary distances: the Wasserstein, Gromov-Wasserstein, and Bures-Wasserstein distances. We examine the closed form of the Wasserstein distance in one dimension via node feature probability distributions, and show how the transport plans of the Wasserstein and Gromov-Wasserstein distances capture which specific nodes influence the distance after graph perturbation. For the Bures-Wasserstein distance, we derive bounds using Laplacian spectra to bypass full spectral decompositions. Finally, we evaluate these distances using a synthetic network dataset for clustering and a real-world time series network for anomaly detection.
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