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Solving Inverse Problems by Joint Posterior Maximization with Autoencoding Prior

arXiv.org Machine Learning

In this work we address the problem of solving ill-posed inverse problems in imaging where the prior is a variational autoencoder (VAE). Specifically we consider the decoupled case where the prior is trained once and can be reused for many different log-concave degradation models without retraining. Whereas previous MAP-based approaches to this problem lead to highly non-convex optimization algorithms, our approach computes the joint (space-latent) MAP that naturally leads to alternate optimization algorithms and to the use of a stochastic encoder to accelerate computations. The resulting technique (JPMAP) performs Joint Posterior Maximization using an Autoencoding Prior. We show theoretical and experimental evidence that the proposed objective function is quite close to bi-convex. Indeed it satisfies a weak bi-convexity property which is sufficient to guarantee that our optimization scheme converges to a stationary point. We also highlight the importance of correctly training the VAE using a denoising criterion, in order to ensure that the encoder generalizes well to out-of-distribution images, without affecting the quality of the generative model. This simple modification is key to providing robustness to the whole procedure. Finally we show how our joint MAP methodology relates to more common MAP approaches, and we propose a continuation scheme that makes use of our JPMAP algorithm to provide more robust MAP estimates. Experimental results also show the higher quality of the solutions obtained by our JPMAP approach with respect to other non-convex MAP approaches which more often get stuck in spurious local optima.


Solving and Learning Nonlinear PDEs with Gaussian Processes

arXiv.org Machine Learning

We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian processes. The proposed approach (1) provides a natural generalization of collocation kernel methods to nonlinear PDEs and IPs, (2) has guaranteed convergence with a path to compute error bounds in the PDE setting, and (3) inherits the state-of-the-art computational complexity of linear solvers for dense kernel matrices. The main idea of our method is to approximate the solution of a given PDE with a MAP estimator of a Gaussian process given the observation of the PDE at a finite number of collocation points. Although this optimization problem is infinite-dimensional, it can be reduced to a finite-dimensional one by introducing additional variables corresponding to the values of the derivatives of the solution at collocation points; this generalizes the representer theorem arising in Gaussian process regression. The reduced optimization problem has a quadratic loss and nonlinear constraints, and it is in turn solved with a variant of the Gauss-Newton method. The resulting algorithm (a) can be interpreted as solving successive linearizations of the nonlinear PDE, and (b) is found in practice to converge in a small number (two to ten) of iterations in experiments conducted on a range of PDEs. For IPs, while the traditional approach has been to iterate between the identifications of parameters in the PDE and the numerical approximation of its solution, our algorithm tackles both simultaneously. Experiments on nonlinear elliptic PDEs, Burgers' equation, a regularized Eikonal equation, and an IP for permeability identification in Darcy flow illustrate the efficacy and scope of our framework.


Learning to Optimize: A Primer and A Benchmark

arXiv.org Machine Learning

Learning to optimize (L2O) is an emerging approach that leverages machine learning to develop optimization methods, aiming at reducing the laborious iterations of hand engineering. It automates the design of an optimization method based on its performance on a set of training problems. This data-driven procedure generates methods that can efficiently solve problems similar to those in the training. In sharp contrast, the typical and traditional designs of optimization methods are theory-driven, so they obtain performance guarantees over the classes of problems specified by the theory. The difference makes L2O suitable for repeatedly solving a certain type of optimization problems over a specific distribution of data, while it typically fails on out-of-distribution problems. The practicality of L2O depends on the type of target optimization, the chosen architecture of the method to learn, and the training procedure. This new paradigm has motivated a community of researchers to explore L2O and report their findings. This article is poised to be the first comprehensive survey and benchmark of L2O for continuous optimization. We set up taxonomies, categorize existing works and research directions, present insights, and identify open challenges.


An inferential perspective on federated learning

AIHub

TL;DR: motivated to better understand the fundamental tradeoffs in federated learning, we present a probabilistic perspective that generalizes and improves upon federated optimization and enables a new class of efficient federated learning algorithms. Thanks to deep learning, today we can train better machine learning models when given access to massive data. However, the standard, centralized training is impossible in many interesting use-cases--due to the associated data transfer and maintenance costs (most notably in video analytics), privacy concerns (e.g., in healthcare settings), or sensitivity of the proprietary data (e.g., in drug discovery). And yet, different parties that own even a small amount of data want to benefit from access to accurate models. This is where federated learning comes to the rescue!


Novel deep learning framework for symbolic regression

#artificialintelligence

Lawrence Livermore National Laboratory (LLNL) computer scientists have developed a new framework and an accompanying visualization tool that leverages deep reinforcement learning for symbolic regression problems, outperforming baseline methods on benchmark problems. The paper was recently accepted as an oral presentation at the International Conference on Learning Representations (ICLR 2021), one of the top machine learning conferences in the world. The conference takes place virtually May 3-7. In the paper, the LLNL team describes applying deep reinforcement learning to discrete optimization--problems that deal with discrete "building blocks" that must be combined in a particular order or configuration to optimize a desired property. The team focused on a type of discrete optimization called symbolic regression--finding short mathematical expressions that fit data gathered from an experiment.


Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges

arXiv.org Machine Learning

Interpretability in machine learning (ML) is crucial for high stakes decisions and troubleshooting. In this work, we provide fundamental principles for interpretable ML, and dispel common misunderstandings that dilute the importance of this crucial topic. We also identify 10 technical challenge areas in interpretable machine learning and provide history and background on each problem. Some of these problems are classically important, and some are recent problems that have arisen in the last few years. These problems are: (1) Optimizing sparse logical models such as decision trees; (2) Optimization of scoring systems; (3) Placing constraints into generalized additive models to encourage sparsity and better interpretability; (4) Modern case-based reasoning, including neural networks and matching for causal inference; (5) Complete supervised disentanglement of neural networks; (6) Complete or even partial unsupervised disentanglement of neural networks; (7) Dimensionality reduction for data visualization; (8) Machine learning models that can incorporate physics and other generative or causal constraints; (9) Characterization of the "Rashomon set" of good models; and (10) Interpretable reinforcement learning. This survey is suitable as a starting point for statisticians and computer scientists interested in working in interpretable machine learning.


BASAR:Black-box Attack on Skeletal Action Recognition

arXiv.org Artificial Intelligence

Skeletal motion plays a vital role in human activity recognition as either an independent data source or a complement. The robustness of skeleton-based activity recognizers has been questioned recently, which shows that they are vulnerable to adversarial attacks when the full-knowledge of the recognizer is accessible to the attacker. However, this white-box requirement is overly restrictive in most scenarios and the attack is not truly threatening. In this paper, we show that such threats do exist under black-box settings too. To this end, we propose the first black-box adversarial attack method BASAR. Through BASAR, we show that adversarial attack is not only truly a threat but also can be extremely deceitful, because on-manifold adversarial samples are rather common in skeletal motions, in contrast to the common belief that adversarial samples only exist off-manifold. Through exhaustive evaluation and comparison, we show that BASAR can deliver successful attacks across models, data, and attack modes. Through harsh perceptual studies, we show that it achieves effective yet imperceptible attacks. By analyzing the attack on different activity recognizers, BASAR helps identify the potential causes of their vulnerability and provides insights on what classifiers are likely to be more robust against attack.


Deep Quantile Aggregation

arXiv.org Machine Learning

Conditional quantile estimation is a key statistical learning challenge motivated by the need to quantify uncertainty in predictions or to model a diverse population without being overly reductive. As such, many models have been developed for this problem. Adopting a meta viewpoint, we propose a general framework (inspired by neural network optimization) for aggregating any number of conditional quantile models in order to boost predictive accuracy. We consider weighted ensembling strategies of increasing flexibility where the weights may vary over individual models, quantile levels, and feature values. An appeal of our approach is its portability: we ensure that estimated quantiles at adjacent levels do not cross by applying simple transformations through which gradients can be backpropagated, and this allows us to leverage the modern deep learning toolkit for building quantile ensembles. Our experiments confirm that ensembling can lead to big gains in accuracy, even when the constituent models are themselves powerful and flexible.


Use of static surrogates in hyperparameter optimization

arXiv.org Artificial Intelligence

Optimizing the hyperparameters and architecture of a neural network is a long yet necessary phase in the development of any new application. This consuming process can benefit from the elaboration of strategies designed to quickly discard low quality configurations and focus on more promising candidates. This work aims at enhancing HyperNOMAD, a library that adapts a direct search derivative-free optimization algorithm to tune both the architecture and the training of a neural network simultaneously, by targeting two keys steps of its execution and exploiting cheap approximations in the form of static surrogates to trigger the early stopping of the evaluation of a configuration and the ranking of pools of candidates. These additions to HyperNOMAD are shown to improve on its resources consumption without harming the quality of the proposed solutions.


Quantum machine learning with differential privacy

arXiv.org Artificial Intelligence

Quantum machine learning (QML) can complement the growing trend of using learned models for a myriad of classification tasks, from image recognition to natural speech processing. A quantum advantage arises due to the intractability of quantum operations on a classical computer. Many datasets used in machine learning are crowd sourced or contain some private information. To the best of our knowledge, no current QML models are equipped with privacy-preserving features, which raises concerns as it is paramount that models do not expose sensitive information. Thus, privacy-preserving algorithms need to be implemented with QML. One solution is to make the machine learning algorithm differentially private, meaning the effect of a single data point on the training dataset is minimized. Differentially private machine learning models have been investigated, but differential privacy has yet to be studied in the context of QML. In this study, we develop a hybrid quantum-classical model that is trained to preserve privacy using differentially private optimization algorithm. This marks the first proof-of-principle demonstration of privacy-preserving QML. The experiments demonstrate that differentially private QML can protect user-sensitive information without diminishing model accuracy. Although the quantum model is simulated and tested on a classical computer, it demonstrates potential to be efficiently implemented on near-term quantum devices (noisy intermediate-scale quantum [NISQ]). The approach's success is illustrated via the classification of spatially classed two-dimensional datasets and a binary MNIST classification. This implementation of privacy-preserving QML will ensure confidentiality and accurate learning on NISQ technology.