Standard causal inference characterizes treatment effect through averages, but the counterfactual distributions could be different in not only the central tendency but also spread and shape. To provide a comprehensive evaluation of treatment effects, we focus on estimating quantile treatment effects (QTEs). Existing methods that invert a nonsmooth estimator of the cumulative distribution functions forbid inference on probability density functions (PDFs), but PDFs can reveal more nuanced characteristics of the counterfactual distributions. We adopt a semiparametric conditional distribution regression model that allows inference on any functionals of counterfactual distributions, including PDFs and multiple QTEs. To account for the observational nature of the data and ensure an efficient model, we adjust for a double balancing score that augments the propensity score with individual covariates. We provide a Bayesian estimation framework that appropriately propagates modeling uncertainty. We show via simulations that the use of double balancing score for confounding adjustment improves performance over adjusting for any single score alone, and the proposed semiparametric model estimates QTEs more accurately than other semiparametric methods. We apply the proposed method to the North Carolina birth weight dataset to analyze the effect of maternal smoking on infant's birth weight.

Rule-based classification models described in the language of logic directly predict boolean values, rather than modeling a probability and translating it into a prediction as done in statistical models. The vast majority of existing uncertainty quantification approaches rely on models providing continuous output not available to rule-based models. In this work, we propose an uncertainty quantification framework in the form of a meta-model that takes any binary classifier with binary output as a black box and estimates the prediction accuracy of that base model at a given input along with a level of confidence on that estimation. The confidence is based on how well that input region is explored and is designed to work in any OOD scenario. We demonstrate the usefulness of this uncertainty model by building an abstaining classifier powered by it and observing its performance in various scenarios.

Unlearn.AI, Inc., 75 Hawthorne St. Ste 560, San Francisco, CA 94105 (Dated: November 7, 2022) Restricted Boltzmann Machines (RBMs) are probabilistic generative models that can be trained by maximum likelihood in principle, but are usually trained by an approximate algorithm called Contrastive Divergence (CD) in practice. In general, a CD-k algorithm estimates an average with respect to the model distribution using a sample obtained from a k-step Markov Chain Monte Carlo Algorithm (e.g., block Gibbs sampling) starting from some initial configuration. Choices of k typically vary from 1 to 100. This technical report explores if it's possible to leverage a simple approximate sampling algorithm with a modified version of CD in order to train an RBM with k=0. As usual, the method is illustrated on MNIST.

Deep learning models for semantic segmentation are prone to poor performance in real-world applications due to the highly challenging nature of the task. Model uncertainty quantification (UQ) is one way to address this issue of lack of model trustworthiness by enabling the practitioner to know how much to trust a segmentation output. Current UQ methods in this application domain are mainly restricted to Bayesian based methods which are computationally expensive and are only able to extract central moments of uncertainty thereby limiting the quality of their uncertainty estimates. We present a simple framework for high-resolution predictive uncertainty quantification of semantic segmentation models that leverages a multi-moment functional definition of uncertainty associated with the model's feature space in the reproducing kernel Hilbert space (RKHS). The multiple uncertainty functionals extracted from this framework are defined by the local density dynamics of the model's feature space and hence automatically align themselves at the tail-regions of the intrinsic probability density function of the feature space (where uncertainty is the highest) in such a way that the successively higher order moments quantify the more uncertain regions. This leads to a significantly more accurate view of model uncertainty than conventional Bayesian methods. Moreover, the extraction of such moments is done in a single-shot computation making it much faster than Bayesian and ensemble approaches (that involve a high number of forward stochastic passes of the model to quantify its uncertainty). We demonstrate these advantages through experimental evaluations of our framework implemented over four different state-of-the-art model architectures that are trained and evaluated on two benchmark road-scene segmentation datasets (Camvid and Cityscapes).

Training energy-based models (EBMs) with noise-contrastive estimation (NCE) is theoretically feasible but practically challenging. Effective learning requires the noise distribution to be approximately similar to the target distribution, especially in high-dimensional domains. Previous works have explored modelling the noise distribution as a separate generative model, and then concurrently training this noise model with the EBM. While this method allows for more effective noise-contrastive estimation, it comes at the cost of extra memory and training complexity. Instead, this thesis proposes a self-adapting NCE algorithm which uses static instances of the EBM along its training trajectory as the noise distribution. During training, these static instances progressively converge to the target distribution, thereby circumventing the need to simultaneously train an auxiliary noise model. Moreover, we express this self-adapting NCE algorithm in the framework of Bregman divergences and show that it is a generalization of maximum likelihood learning for EBMs. The performance of our algorithm is evaluated across a range of noise update intervals, and experimental results show that shorter update intervals are conducive to higher synthesis quality.

We study the convergence of several natural policy gradient (NPG) methods in infinite-horizon discounted Markov decision processes with regular policy parametrizations. For a variety of NPGs and reward functions we show that the trajectories in state-action space are solutions of gradient flows with respect to Hessian geometries, based on which we obtain global convergence guarantees and convergence rates. In particular, we show linear convergence for unregularized and regularized NPG flows with the metrics proposed by Kakade and Morimura and co-authors by observing that these arise from the Hessian geometries of conditional entropy and entropy respectively. Further, we obtain sublinear convergence rates for Hessian geometries arising from other convex functions like log-barriers. Finally, we interpret the discrete-time NPG methods with regularized rewards as inexact Newton methods if the NPG is defined with respect to the Hessian geometry of the regularizer. This yields local quadratic convergence rates of these methods for step size equal to the penalization strength.

The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a Convolutional Autoencoder for dimensionality reduction and a classifier composed by a Fully Connected Network, are combined to simultaneously produce supervised dimensionality reduction and predictions. It turned out that this methodology can also be greatly beneficial in enforcing explainability of deep learning architectures. Additionally, the resulting Latent Space, optimized for the classification task, can be utilized to improve traditional, interpretable classification algorithms. The experimental results, showed that the proposed methodology achieved competitive results against the state of the art deep learning methods, while being much more efficient in terms of parameter count. Finally, it was empirically justified that the proposed methodology introduces advanced explainability regarding, not only the data structure through the produced latent space, but also about the classification behaviour.

This paper is concerned with constructing a confidence interval for a target policy's value offline based on a pre-collected observational data in infinite horizon settings. Most of the existing works assume no unmeasured variables exist that confound the observed actions. This assumption, however, is likely to be violated in real applications such as healthcare and technological industries. In this paper, we show that with some auxiliary variables that mediate the effect of actions on the system dynamics, the target policy's value is identifiable in a confounded Markov decision process. Based on this result, we develop an efficient off-policy value estimator that is robust to potential model misspecification and provide rigorous uncertainty quantification. Our method is justified by theoretical results, simulated and real datasets obtained from ridesharing companies. A Python implementation of the proposed procedure is available at https://github.com/Mamba413/cope.

Music is one of the Gardner's intelligences in his theory of multiple intelligences. How humans perceive and understand music is still being studied and is crucial to develop artificial intelligence models that imitate such processes. Music generation with Artificial Intelligence is an emerging field that is gaining much attention in the recent years. In this paper, we describe how humans compose music and how new AI systems could imitate such process by comparing past and recent advances in the field with music composition techniques. To understand how AI models and algorithms generate music and the potential applications that might appear in the future, we explore, analyze and describe the agents that take part of the music generation process: the datasets, models, interfaces, the users and the generated music. We mention possible applications that might benefit from this field and we also propose new trends and future research directions that could be explored in the future.

The rise of big data analytics has automated the decision-making of companies and increased supply chain agility. In this paper, we study the supply chain contract design problem faced by a data-driven supplier who needs to respond to the inventory decisions of the downstream retailer. Both the supplier and the retailer are uncertain about the market demand and need to learn about it sequentially. The goal for the supplier is to develop data-driven pricing policies with sublinear regret bounds under a wide range of possible retailer inventory policies for a fixed time horizon. To capture the dynamics induced by the retailer's learning policy, we first make a connection to non-stationary online learning by following the notion of variation budget. The variation budget quantifies the impact of the retailer's learning strategy on the supplier's decision-making. We then propose dynamic pricing policies for the supplier for both discrete and continuous demand. We also note that our proposed pricing policy only requires access to the support of the demand distribution, but critically, does not require the supplier to have any prior knowledge about the retailer's learning policy or the demand realizations. We examine several well-known data-driven policies for the retailer, including sample average approximation, distributionally robust optimization, and parametric approaches, and show that our pricing policies lead to sublinear regret bounds in all these cases. At the managerial level, we answer affirmatively that there is a pricing policy with a sublinear regret bound under a wide range of retailer's learning policies, even though she faces a learning retailer and an unknown demand distribution. Our work also provides a novel perspective in data-driven operations management where the principal has to learn to react to the learning policies employed by other agents in the system.