Given the ever-increasing computational costs of modern machine learning models, we need to find new ways to reuse such expert models and thus tap into the resources that have been invested in their creation. Recent work suggests that the power of these massive models is captured by the representations they learn. Therefore, we seek a model that can relate between different existing representations and propose to solve this task with a conditionally invertible network. This network demonstrates its capability by (i) providing generic transfer between diverse domains, (ii) enabling controlled content synthesis by allowing modification in other domains, and (iii) facilitating diagnosis of existing representations by translating them into interpretable domains such as images. Our domain transfer network can translate between fixed representations without having to learn or finetune them. This allows users to utilize various existing domain-specific expert models from the literature that had been trained with extensive computational resources. Experiments on diverse conditional image synthesis tasks, competitive image modification results and experiments on image-to-image and text-to-image generation demonstrate the generic applicability of our approach. For example, we translate between BERT and BigGAN, state-of-the-art text and image models to provide text-to-image generation, which neither of both experts can perform on their own.

One of the common ways children learn is by mimicking adults. Imitation learning focuses on learning policies with suitable performance from demonstrations generated by an expert, with an unspecified performance measure, and unobserved reward signal. Popular methods for imitation learning start by either directly mimicking the behavior policy of an expert (behavior cloning) or by learning a reward function that prioritizes observed expert trajectories (inverse reinforcement learning). However, these methods rely on the assumption that covariates used by the expert to determine her/his actions are fully observed. In this paper, we relax this assumption and study imitation learning when sensory inputs of the learner and the expert differ. First, we provide a non-parametric, graphical criterion that is complete (both necessary and sufficient) for determining the feasibility of imitation from the combinations of demonstration data and qualitative assumptions about the underlying environment, represented in the form of a causal model. We then show that when such a criterion does not hold, imitation could still be feasible by exploiting quantitative knowledge of the expert trajectories. Finally, we develop an efficient procedure for learning the imitating policy from experts' trajectories.

The Gumbel-Max trick is the basis of many relaxed gradient estimators. These estimators are easy to implement and low variance, but the goal of scaling them comprehensively to large combinatorial distributions is still outstanding. Working within the perturbation model framework, we introduce stochastic softmax tricks, which generalize the Gumbel-Softmax trick to combinatorial spaces. Our framework is a unified perspective on existing relaxed estimators for perturbation models, and it contains many novel relaxations. We design structured relaxations for subset selection, spanning trees, arborescences, and others. When compared to less structured baselines, we find that stochastic softmax tricks can be used to train latent variable models that perform better and discover more latent structure.

Causal discovery aims to recover causal structures or models underlying the observed data. Despite its success in certain domains, most existing methods focus on causal relations between observed variables, while in many scenarios the observed ones may not be the underlying causal variables (e.g., image pixels), but are generated by latent causal variables or confounders that are causally related. To this end, in this paper, we consider Linear, Non-Gaussian Latent variable Models (LiNGLaMs), in which latent confounders are also causally related, and propose a Generalized Independent Noise (GIN) condition to estimate such latent variable graphs. Specifically, for two observed random vectors $\mathbf{Y}$ and $\mathbf{Z}$, GIN holds if and only if $\omega^{\intercal}\mathbf{Y}$ and $\mathbf{Z}$ are statistically independent, where $\omega$ is a parameter vector characterized from the cross-covariance between $\mathbf{Y}$ and $\mathbf{Z}$. From the graphical view, roughly speaking, GIN implies that causally earlier latent common causes of variables in $\mathbf{Y}$ d-separate $\mathbf{Y}$ from $\mathbf{Z}$. Interestingly, we find that the independent noise condition, i.e., if there is no confounder, causes are independent from the error of regressing the effect on the causes, can be seen as a special case of GIN. Moreover, we show that GIN helps locate latent variables and identify their causal structure, including causal directions. We further develop a recursive learning algorithm to achieve these goals. Experimental results on synthetic and real-world data demonstrate the effectiveness of our method.

Given a discrete probability measure supported on $N$ atoms and a set of $n$ real-valued functions, there exists a probability measure that is supported on a subset of $n+1$ of the original $N$ atoms and has the same mean when integrated against each of the $n$ functions. If $ N \gg n$ this results in a huge reduction of complexity. We give a simple geometric characterization of barycenters via negative cones and derive a randomized algorithm that computes this new measure by ``greedy geometric sampling''. We then study its properties, and benchmark it on synthetic and real-world data to show that it can be very beneficial in the $N\gg n$ regime. A Python implementation is available at \url{https://github.com/FraCose/Recombination_Random_Algos}.

Design of experiments and estimation of treatment effects in large-scale networks, in the presence of strong interference, is a challenging and important problem. Most existing methods' performance deteriorates as the density of the network increases. In this paper, we present a novel strategy for accurately estimating the causal effects of a class of treatments in a dense large-scale network. First, we design an approximate randomized controlled experiment by solving an optimization problem to allocate treatments in the presence of competition among neighboring nodes. Then we apply an importance sampling adjustment to correct for any leftover bias (from the approximation) in estimating average treatment effects. We provide theoretical guarantees, verify robustness in a simulation study, and validate the scalability and usefulness of our procedure in a real-world experiment on a large social network.

Training models with discrete latent variables is challenging due to the difficulty of estimating the gradients accurately. Much of the recent progress has been achieved by taking advantage of continuous relaxations of the system, which are not always available or even possible. The Augment-REINFORCE-Merge (ARM) estimator provides an alternative that, instead of relaxation, uses continuous augmentation. Applying antithetic sampling over the augmenting variables yields a relatively low-variance and unbiased estimator applicable to any model with binary latent variables. However, while antithetic sampling reduces variance, the augmentation process increases variance. We show that ARM can be improved by analytically integrating out the randomness introduced by the augmentation process, guaranteeing substantial variance reduction. Our estimator, DisARM, is simple to implement and has the same computational cost as ARM. We evaluate DisARM on several generative modeling benchmarks and show that it consistently outperforms ARM and a strong independent sample baseline in terms of both variance and log-likelihood. Furthermore, we propose a local version of DisARM designed for optimizing the multi-sample variational bound, and show that it outperforms VIMCO, the current state-of-the-art method.

We consider the evaluation and training of a new policy for the evaluation data by using the historical data obtained from a different policy. The goal of off-policy evaluation (OPE) is to estimate the expected reward of a new policy over the evaluation data, and that of off-policy learning (OPL) is to find a new policy that maximizes the expected reward over the evaluation data. Although the standard OPE and OPL assume the same distribution of covariate between the historical and evaluation data, there often exists a problem of a covariate shift,i.e., the distribution of the covariate of the historical data is different from that of the evaluation data. In this paper, we derive the efficiency bound of OPE under a covariate shift. Then, we propose doubly robust and efficient estimators for OPE and OPL under a covariate shift by using an estimator of the density ratio between the distributions of the historical and evaluation data. We also discuss other possible estimators and compare their theoretical properties. Finally, we confirm the effectiveness of the proposed estimators through experiments.

It is a truth universally acknowledged that an observed association without known mechanism must be in want of a causal estimate. Causal estimates from observational data will be biased in the presence of ‘unobserved confounding’. However, we might hope that the influence of unobserved confounders is weak relative to a ‘large’ estimated effect. The purpose of this paper is to develop Austen plots, a sensitivity analysis tool to aid such judgments by making it easier to reason about potential bias induced by unobserved confounding. We formalize confounding strength in terms of how strongly the unobserved confounding influences treatment assignment and outcome. For a target level of bias, an Austen plot shows the minimum values of treatment and outcome influence required to induce that level of bias. Austen plots generalize the classic sensitivity analysis approach of Imbens [Imb03]. Critically, Austen plots allow any approach for modeling the observed data. We illustrate the tool by assessing biases for several real causal inference problems, using a variety of machine learning approaches for the initial data analysis. Code, demo data, and a tutorial are available at github.com/anishazaveri/austen_plots.

Learning a causal directed acyclic graph from data is a challenging task that involves solving a combinatorial problem for which the solution is not always identifiable. A new line of work reformulates this problem as a continuous constrained optimization one, which is solved via the augmented Lagrangian method. However, most methods based on this idea do not make use of interventional data, which can significantly alleviate identifiability issues. This work constitutes a new step in this direction by proposing a theoretically-grounded method based on neural networks that can leverage interventional data. We illustrate the flexibility of the continuous-constrained framework by taking advantage of expressive neural architectures such as normalizing flows. We show that our approach compares favorably to the state of the art in a variety of settings, including perfect and imperfect interventions for which the targeted nodes may even be unknown.

Multivariate zero-inflated count data arise in a wide range of areas such as economics, social sciences, and biology. To infer causal relationships in zero-inflated count data, we propose a new zero-inflated Poisson Bayesian network (ZIPBN) model. We show that the proposed ZIPBN is identifiable with cross-sectional data. The proof is based on the well-known characterization of Markov equivalence class which is applicable to other distribution families. For causal structural learning, we introduce a fully Bayesian inference approach which exploits the parallel tempering Markov chain Monte Carlo algorithm to efficiently explore the multi-modal network space. We demonstrate the utility of the proposed ZIPBN in causal discoveries for zero-inflated count data by simulation studies with comparison to alternative Bayesian network methods. Additionally, real single-cell RNA-sequencing data with known causal relationships will be used to assess the capability of ZIPBN for discovering causal relationships in real-world problems.

Probabilistic inference in pairwise Markov Random Fields (MRFs), i.e. computing the partition function or computing a MAP estimate of the variables, is a foundational problem in probabilistic graphical models. Semidefinite programming relaxations have long been a theoretically powerful tool for analyzing properties of probabilistic inference, but have not been practical owing to the high computational cost of typical solvers for solving the resulting SDPs. In this paper, we propose an efficient method for computing the partition function or MAP estimate in a pairwise MRF by instead exploiting a recently proposed coordinate-descent-based fast semidefinite solver. We also extend semidefinite relaxations from the typical binary MRF to the full multi-class setting, and develop a compact semidefinite relaxation that can again be solved efficiently using the solver. We show that the method substantially outperforms (both in terms of solution quality and speed) the existing state of the art in approximate inference, on benchmark problems drawn from previous work. We also show that our approach can scale to large MRF domains such as fully-connected pairwise CRF models used in computer vision.