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Directed acyclic graph models with hidden variables have been much studied, particularly in view of their computational efficiency and connection with causal methods. In this paper we provide the circumstances under which it is possible for two variables to be identically equal, while all other observed variables stay jointly independent of them and mutually of each other. We find that this is possible if and only if the two variables are `densely connected&#39;; in other words, if applications of identifiable causal interventions on the graph cannot (non-trivially) separate them. As a consequence of this, we can also allow such pairs of random variables have any bivariate joint distribution that we choose. This has implications for model search, since it suggests that we can reduce to only consider graphs in which densely connected vertices are always joined by an edge.

UAI 2021

Dependency in DAG models with Hidden Variables

latent variables

directed acylic graphs

nested markov property

graphical models

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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A ticket is required to access this conference. Please use the provided link to register for the event.

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/)

Directed acyclic graph models with hidden variables have been much studied, particularly in view of their computational efficiency and connection with causal methods. In this paper we provide the circumstances under which it is possible for two variables to be identically equal, while all other observed variables stay jointly independent of them and mutually of each other. We find that this is possible if and only if the two variables are `densely connected'; in other words, if applications of identifiable causal interventions on the graph cannot (non-trivially) separate them. As a consequence of this, we can also allow such pairs of random variables have any bivariate joint distribution that we choose. This has implications for model search, since it suggests that we can reduce to only consider graphs in which densely connected vertices are always joined by an edge.

lightning talk

In many real-world scenarios, such as gene knockout experiments, targeted interventions are often accompanied by unknown interventions at off-target sites. Moreover, different units can get randomly exposed to different unknown interventions, thereby creating a mixture of interventions. Identifying different components of this mixture can be very valuable in some applications. Motivated by such situations, in this work, we study the problem of identifying all components present in a mixture of interventions on a given causal Bayesian Network. We construct an example to show that, in general, the components are not identifiable from the mixture distribution. Next, assuming that the given network satisfies a positivity condition, we show that, if the set of mixture components satisfy a mild exclusion assumption, then they can be uniquely identified. Our proof gives an efficient algorithm to recover these targets from the exponentially large search space of possible targets. In the more realistic scenario, where distributions are given via finitely many samples, we conduct a simulation study to analyze the performance of an algorithm derived from our identifiability proof.

Disentangling Mixtures of Unknown Causal Interventions

Density ratio estimation serves as an important technique in the unsupervised machine learning toolbox. However, such ratios are difficult to estimate for complex, high-dimensional data, particularly when the densities of interest are sufficiently different. In our work, we propose to leverage an invertible generative model to map the two distributions into a common feature space prior to estimation. This featurization brings the densities closer together in latent space, sidestepping pathological scenarios where the learned density ratios in input space can be arbitrarily inaccurate. At the same time, the invertibility of our feature map guarantees that the ratios computed in feature space are equivalent to those in input space. Empirically, we demonstrate the efficacy of our approach in a variety of downstream tasks that require access to accurate density ratios such as mutual information estimation, targeted sampling in deep generative models, and classification with data augmentation.

Featurized Density Ratio Estimation

We propose a new generative modeling technique for learning multidimensional cumulative distribution functions (CDFs) in the form of copulas. Specifically, we consider certain classes of copulas known as Archimedean and hierarchical Archimedean copulas, popular for their parsimonious representation and ability to model different tail dependencies. We consider their representation as mixture models with Laplace transforms of latent random variables from generative neural networks. This alternative representation allows for computational efficiencies and easy sampling, especially in high dimensions. We describe multiple methods for optimizing the network parameters. Finally, we present empirical results that demonstrate the efficacy of our proposed method in learning multidimensional CDFs and its computational efficiency compared to existing methods.

Generative Archimedean Copulas

There has been growing interest in the AI community for precise uncertainty quantification. Conditional density models f(y|x), where x represents potentially high-dimensional features, are an integral part of uncertainty quantification in prediction and Bayesian inference. However, it is challenging to assess conditional density estimates and gain insight into modes of failure. While existing diagnostic tools can determine whether an approximated conditional density is compatible overall with a data sample, they lack a principled framework for identifying, locating, and interpreting the nature of statistically significant discrepancies over the entire feature space. In this paper, we present rigorous and easy-to-interpret diagnostics such as (i) the "Local Coverage Test" (LCT), which distinguishes an arbitrarily misspecified model from the true conditional density of the sample, and (ii) "Amortized Local P-P plots" (ALP) which can quickly provide interpretable graphical summaries of distributional differences at any location x in the feature space. Our validation procedures scale to high dimensions and can potentially adapt to any type of data at hand. We demonstrate the effectiveness of LCT and ALP through a simulated experiment and applications to prediction and parameter inference for image data.

Diagnostics for Conditional Density Models and Bayesian Inference Algorithms

In representation learning, capturing correlations between the represented elements is paramount. A recent line of work introduces the notion of learning region-based representations, with the objective of being able to better capture these correlations as set interactions. Box models use regions which are products of intervals on $[0,1]$ (i.e., "boxes"), representing joint probability distributions via Lebesgue measure. To mitigate issues with training, a recent work models the endpoints of these intervals using Gumbel distributions, chosen due to their min/max-stability.

Min/Max Stability and Box Distributions

Being aware of observers and the inferences they make about an agent's behavior is crucial for successful multi-agent interaction.

A Unifying Framework for Observer-Aware Planning and its Complexity

We study the statistical seriation problem, where the goal is to estimate a matrix whose rows satisfy the same shape constraint after a permutation of the columns. This is a important classical problem, with close connections to statistical literature in permutation-based models and also has wide applications ranging from archaeology to biology. Specifically, we consider the case where the rows are monotonically increasing after an unknown permutation of the columns. Past work has shown that the least-squares estimator is optimal up to logarithmic factors, but efficient algorithms for computing the least-squares estimator remain unknown to date. We approach this important problem from a heuristic perspective. Specifically, we replace the combinatorial permutation constraint by a continuous regularization term, and then use projected gradient descent to obtain a local minimum of the non-convex objective. We show that the attained local minimum is the global minimum in certain special cases under the noiseless setting, and preserves desirable properties under the noisy setting. Simulation results reveal that our proposed algorithm outperforms prior algorithms when (1) the underlying model is more complex than simplistic parametric assumptions such as low-rankedness, or (2) the signal-to-noise ratio is high. Under partial observations, the proposed algorithm requires an initialization, and different initializations may lead to different local minima. We empirically observe that the proposed algorithm yields consistent improvement over the initialization, even though different initializations start with different levels of quality.

A Heuristic for Statistical Seriation

Neural architecture search (NAS) has seen a steep rise in interest over the last few years. Many algorithms for NAS consist of searching through a space of architectures by iteratively choosing an architecture, evaluating its performance by training it, and using all prior evaluations to come up with the next choice. The evaluation step is noisy - the final accuracy varies based on the random initialization of the weights. Prior work has focused on devising new search algorithms to handle this noise, rather than quantifying or understanding the level of noise in architecture evaluations. In this work, we show that (1) the simplest hill-climbing algorithm is a powerful baseline for NAS, and (2), when the noise in popular NAS benchmark datasets is reduced to a minimum, hill-climbing to outperforms many popular state-of-the-art algorithms. We further back up this observation by showing that the number of local minima is substantially reduced as the noise decreases, and by giving a theoretical characterization of the performance of local search in NAS. Based on our findings, for NAS research we suggest (1) using local search as a baseline, and (2) denoising the training pipeline when possible.

Exploring the Loss Landscape in Neural Architecture Search

Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) approach that exhibits favourable exploration properties in high-dimensional models such as neural networks. Unfortunately, HMC has limited use in large-data regimes and little work has explored suitable approaches that aim to preserve the entire Hamiltonian. In our work, we introduce a new symmetric integration scheme for split HMC that does not rely on stochastic gradients. We show that our new formulation is more efficient than previous approaches and is easy to implement with a single GPU. As a result, we are able to perform full HMC over common deep learning architectures using entire data sets. In addition, when we compare with stochastic gradient MCMC, we show that our method achieves better performance in both accuracy and uncertainty quantification. Our approach demonstrates HMC as a feasible option when considering inference schemes for large-scale machine learning problems.

Scaling Hamiltonian Monte Carlo Inference for Bayesian Neural Networks with Symmetric Splitting

Active search refers to the problem of efficiently locating targets in an unknown environment by actively making data-collection decisions. In this paper, we are focusing on multiple aerial robots (agents) detecting targets such as gas leaks, radiation sources or human survivors of disasters. One of the main challenges of active search with multiple agents in unknown environments is impracticality of central coordination due to the difficulties of connectivity maintenance. In this paper, we propose two distinct active search algorithms that allow for multiple robots to independently make data-collection decisions without a central coordinator. Throughout we consider that targets are sparsely located around the environment in keeping with compressive sensing assumptions and its applicability

Dependency in DAG models with Hidden Variables

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