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Peter Orbanz

Peter Orbanz appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Machine Learningmath.STStatistics Theorymath.PRmath.CO

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Published work

7 published item(s)

preprint2026arXiv

Debiased Counterfactual Generation via Flow Matching from Observations

Estimating counterfactual distributions under interventions is central to treatment risk assessment and counterfactual generation tasks. Existing approaches model the counterfactual distribution as a standalone generative target, without exploiting its relationship to the observational data. In this work, we show that under standard assumptions, observational and counterfactual outcome distributions are tightly linked: they have identical support and tail behavior, remain statistically close under weak confounding, and share any features of high-dimensional outcomes which are invariant to confounders. These properties motivate learning counterfactual distributions not from scratch, but via a deconfounding flow from the observational distribution. We formulate this problem via flow-matching and derive a semiparametrically efficient estimator based on a novel efficient influence function correction. We subsequently extend our estimator to target minimal-energy flows in high-dimensions, which we show can be especially simple targets between observational and counterfactual distributions. In experiments, deconfounding flows outperform existing debiased counterfactual distribution estimators, while also mitigating known failure modes of flow-based methods.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Uniform estimation in stochastic block models is slow

We explicitly quantify the empirically observed phenomenon that estimation under a stochastic block model (SBM) is hard if the model contains classes that are similar. More precisely, we consider estimation of certain functionals of random graphs generated by a SBM. The SBM may or may not be sparse, and the number of classes may be fixed or grow with the number of vertices. Minimax lower and upper bounds of estimation along specific submodels are derived. The results are nonasymptotic and imply that uniform estimation of a single connectivity parameter is much slower than the expected asymptotic pointwise rate. Specifically, the uniform quadratic rate does not scale as the number of edges, but only as the number of vertices. The lower bounds are local around any possible SBM. An analogous result is derived for functionals of a class of smooth graphons.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Bayesian Models of Graphs, Arrays and Other Exchangeable Random Structures

The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and many other parametric and nonparametric Bayesian models fall within the remit of this framework; many problems arising in modern data analysis do not. This article provides an introduction to Bayesian models of graphs, matrices, and other data that can be modeled by random structures. We describe results in probability theory that generalize de Finetti's theorem to such data and discuss their relevance to nonparametric Bayesian modeling. With the basic ideas in place, we survey example models available in the literature; applications of such models include collaborative filtering, link prediction, and graph and network analysis. We also highlight connections to recent developments in graph theory and probability, and sketch the more general mathematical foundation of Bayesian methods for other types of data beyond sequences and arrays.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Scaled subordinators and generalizations of the Indian buffet process

We study random families of subsets of $\mathbb{N}$ that are similar to exchangeable random partitions, but do not require constituent sets to be disjoint: Each element of ${\mathbb{N}}$ may be contained in multiple subsets. One class of such objects, known as Indian buffet processes, has become a popular tool in machine learning. Based on an equivalence between Indian buffet and scale-invariant Poisson processes, we identify a random scaling variable whose role is similar to that played in exchangeable partition models by the total mass of a random measure. Analogous to the construction of exchangeable partitions from normalized subordinators, random families of sets can be constructed from randomly scaled subordinators. Coupling to a heavy-tailed scaling variable induces a power law on the number of sets containing the first $n$ elements. Several examples, with properties desirable in applications, are derived explicitly. A relationship to exchangeable partitions is made precise as a correspondence between scaled subordinators and Poisson-Kingman measures, generalizing a result of Arratia, Barbour and Tavare on scale-invariant processes.

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preprint2011arXiv

Conjugate Projective Limits

We characterize conjugate nonparametric Bayesian models as projective limits of conjugate, finite-dimensional Bayesian models. In particular, we identify a large class of nonparametric models representable as infinite-dimensional analogues of exponential family distributions and their canonical conjugate priors. This class contains most models studied in the literature, including Dirichlet processes and Gaussian process regression models. To derive these results, we introduce a representation of infinite-dimensional Bayesian models by projective limits of regular conditional probabilities. We show under which conditions the nonparametric model itself, its sufficient statistics, and -- if they exist -- conjugate updates of the posterior are projective limits of their respective finite-dimensional counterparts. We illustrate our results both by application to existing nonparametric models and by construction of a model on infinite permutations.

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preprint2011arXiv

Projective Limit Random Probabilities on Polish Spaces

A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be constructed from their finite-dimensional marginals---the most prominent example being the construction of the Dirichlet process from finite-dimensional Dirichlet distributions. This approach is both intuitive and applicable to the construction of arbitrary distributions on M(V), but also hamstrung by a number of technical difficulties. We show how these difficulties can be resolved if the domain V is a Polish topological space, and give a representation theorem directly applicable to the construction of any probability distribution on M(V) whose first moment measure is well-defined. The proof draws on a projective limit theorem of Bochner, and on properties of set functions on Polish spaces to establish countable additivity of the resulting random probabilities.

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