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In this paper, we study the differentially private Principal Component Analysis (PCA) problem in stochastic optimization settings. We first propose

UAI 2021

Principal Component Analysis in the Stochastic Differential Privacy Model

stochastic optimization

principal component analysis

differential privacy

The Conference on Uncertainty in Artificial Intelligence (UAI) is one of the premier international conferences on research related to knowledge representation, learning, and reasoning in the presence of uncertainty. It is supported by the [Association for Uncertainty in Artificial Intelligence (AUAI).](https://www.auai.org/)

The 37th Conference on Uncertainty in Artificial Intelligence (UAI 2021) is held fully online. We have an exciting program consisting of keynote talks by [Susan Murphy](https://www.auai.org/uai2021/program?block=A), [Eric Horvitz](https://www.auai.org/uai2021/program?block=B), [Lenka Zdeborová](https://www.auai.org/uai2021/program?block=C), [Judea Pearl](https://www.auai.org/uai2021/program?block=D) and [Ankur Moitra](https://www.auai.org/uai2021/program?block=E), a town hall meeting, peer-reviewed papers, and three workshops. The main conference is single-track and each paper is show-cased with a live component (either a live discussion and Q&A, or a live lightning talk). All papers are also featured in video presentations and in poster sessions in gather.town. The three parallel workshops on Friday allow for smaller meetings on current topics.

The walkthrough video below shows how you can navigate this site and use the different possibilities for interaction: UAIsland2021 on gather.town for posters and social interactions, the mementor platform for virtual mentoring sessions, and the chat and Q&A systems for discussions about talks and posters.

Have a great UAI 2021! 
<br>
<br>Cassio de Campos and Marloes Maathuis
<br>UAI 2021 Program Chairs
<br>uai2021programchairs@gmail.com

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https://auai.org/uai2021/registration

The Conference on Uncertainty in Artificial Intelligence (UAI) is one of the premier international conferences on research related to knowledge representation, learning, and reasoning in the presence of uncertainty. It is supported by the [Association for Uncertainty in Artificial Intelligence (AUAI).](https://www.auai.org/)

technical paper

This paper describes a new probabilistic generative model for noisy, sparse, and heterogeneous relational data called the hierarchical infinite relational model (HIRM). Given a set of relations defined over a collection of domains, the model first infers multiple non-overlapping clusters of relations using a top-level Chinese restaurant process. Within each cluster of relations, a Dirichlet process mixture is then used to partition the domain entities and model the probability distribution of relation values. The HIRM generalizes the standard infinite relational model and can be used for a variety of data analysis tasks including dependence detection, clustering, and density estimation. We present new algorithms for fully Bayesian posterior inference via Gibbs sampling. We illustrate the efficacy of the method on a density estimation benchmark of twenty object-attribute datasets with up to 18 million cells and use it to discover relational structure in real-world datasets from politics and genomics.

Hierarchical Infinite Relational Model

We present a new non-negative matrix factorization model for $(0,1)$

Doubly Non-Central Beta Matrix Factorization for DNA Methylation Data

Hierarchical clustering is a critical task in numerous domains. Many approaches are based on heuristics and the properties of the resulting clusterings are studied post hoc. However, in several applications, there is a natural cost function that can be used to characterize the quality of the clustering. In those cases, hierarchical clustering can be seen as a combinatorial optimization problem. To that end, we introduce a new approach based on A* search. We overcome the prohibitively large search space by combining A* with a novel trellis data structure. This results in an exact algorithm that scales beyond previous state of the art (from search space with 10^12 trees to 10^15 trees) and an approximate algorithm that improves over baselines, even in enormous search spaces (that contain more than 10^1000 trees). Empirically we demonstrate that our method achieves substantially higher quality results than baselines for a particle physics use case and other clustering benchmarks. We describe how our method provides significantly improved theoretical bounds on the time and space complexity of A* for clustering.

Exact and Approximate Hierarchical Clustering Using A*

Parametric path problems arise independently in diverse domains, ranging from transportation to finance, where they are studied under various assumptions. We formulate a general path problem with relaxed assumptions, and describe how this formulation is applicable in these domains.

Generalized Parametric Path Problems

Machine-learning models contain information about the data they were trained

Measuring Data Leakage in Machine-Learning Models with Fisher Information

Structural causal models postulate noisy functional relations among a set of interacting variables. The causal structure underlying each such model is naturally represented by a directed graph whose edges indicate for each variable which other variables it causally depends upon. Under a number of different model assumptions, it has been shown that this causal graph and, thus also, causal effects are identifiable from mere observational data. For these models, practical algorithms have been devised to learn the graph. Moreover, when the graph is known, standard techniques may be used to give estimates and confidence intervals for causal effects. We argue, however, that a two-step method that first learns a graph and then treats the graph as known yields confidence intervals that are overly optimistic and can drastically fail to account for the uncertain causal structure. To address this issue we lay out a framework based on test inversion that allows us to give confidence regions for total causal effects that capture both sources of uncertainty: causal structure and numerical size of nonzero effects. Our ideas are developed in the context of bivariate linear causal models with homoscedastic errors, but as we exemplify they are generalizable to larger systems as well as other settings such as, in particular, linear non-Gaussian models.

Confidence in Causal Discovery with Linear Causal Models

Updating observations of a signal due to the delays in the measurement process is a common problem in signal processing, with prominent examples in a wide range of fields.

Gaussian Process Nowcasting: Application to COVID-19 Mortality Reporting

We present a novel model for capturing the behavior of an agent exhibiting sunk-cost bias in a stochastic environment. Agents exhibiting sunk-cost bias take into account the effort they have already spent on an endeavor when they evaluate whether to continue or abandon it. We model planning tasks in which an agent with this type of bias tries to reach a designated goal. Our model structures this problem as a type of Markov decision process: loosely speaking, the agent traverses a directed acyclic graph with probabilistic transitions, paying costs for its actions as it tries to reach a target node containing a specified reward. The agent's sunk cost bias is modeled by a cost that it incurs for abandoning the traversal: if the agent decides to stop traversing the graph, it incurs a cost of $\lambda \cdot C_{sunk}$, where ${\lambda \geq 0}$ is a parameter that captures the extent of the bias and $C_{sunk}$ is the sum of costs already invested.

Stochastic Model for Sunk Cost Bias

Auxiliary particle filters (APFs) are a class of sequential Monte Carlo (SMC) methods for Bayesian inference in state-space models. In their original derivation, APFs operate in an extended state space using an auxiliary variable to improve inference. In this work, we propose optimized auxiliary particle filters, a framework where the traditional APF auxiliary variables are interpreted as weights in a importance sampling mixture proposal. Under this interpretation, we devise a mechanism for proposing the mixture weights that is inspired by recent advances in multiple and adaptive importance sampling. In particular, we propose to select the mixture weights by formulating a convex optimization problem, with the aim of approximating the filtering posterior at each timestep. Further, we propose a weighting scheme that generalizes previous results on the APF (Pitt et al. 2012), proving unbiasedness and consistency of our estimators. Our framework demonstrates significantly improved estimates on a range of metrics compared to state-of-the-art particle filters at similar computational complexity in challenging and widely used dynamical models.

Optimized Auxiliary Particle Filters

Conventional methods in causal effect inferencetypically rely on specifying a valid set of control variables. When this set is unknown or misspecified, inferences will be erroneous. We propose a method for inferring average causal effects when all potential confounders are observed, but thecontrol variables are unknown. When the data-generating process belongs to the class of acyclical linear structural causal models, we prove that themethod yields asymptotically valid confidence intervals. Our results build upon a smooth characterization of linear directed acyclic graphs. We verify the capability of the method to produce valid confidence intervals for average causal effects using synthetic data, even when the appropriate specification of control variables is unknown.

Principal Component Analysis in the Stochastic Differential Privacy Model

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