We study the problem of exact completion for $m \times n$ sized matrix of rank r with the adaptive sampling method. We introduce a relation of the exact completion problem with the sparsest vector of column and row spaces (which we call sparsity-number here). Using this relation, we propose matrix completion algorithms that exactly recovers the target matrix. These algorithms are superior to previous works in two important ways. First, our algorithms exactly recover $\mu_0$-coherent column space matrices by probability at least $1-\epsilon$ using much smaller observations complexity than - $\mathcal{O}(\mu_0 rn \mathrm{log}\frac{r}{\epsilon})$ - the state of art. Specifically, many of the previous adaptive sampling methods require to observe the entire matrix when the column space is highly coherent. However, we show that our method is still able to recover this type of matrices by observing a small fraction of entries under many scenarios. Second, we propose an exact completion algorithm, which requires minimal pre-information as either row or column space is not being highly coherent. We provide an extension of these algorithms that is robust to sparse random noise. Besides, we propose an additional low-rank estimation algorithm that is robust to any small noise by adaptively studying the shape of column space. At the end of the paper, we provide experimental results that illustrate the strength of the algorithms proposed here.

Program synthesis has recently emerged as a promising approach to the image parsing task. However, most prior works have relied on supervised learning methods, which require ground truth programs for each training image. We present an unsupervised learning algorithm that can parse constructive solid geometry (CSG) images into context-free grammar with a non-differentiable renderer. We propose a grammar-encoded tree LSTM to effectively constrain our search space by leveraging the structure of the context-free grammar while handling the non-differentiable renderer via REINFORCE and encouraging the exploration by regularizing the objective with an entropy term. Instead of using simple Monte Carlo sampling, we propose a lower-variance entropy estimator with sampling without replacement for effective exploration. We demonstrate the effectiveness of the proposed algorithm on a synthetic 2D CSG dataset, which outperforms baseline models by a large margin.

We explore the intersection of human and machine creativity by generating sculptural objects through machine learning. This research raises questions about both the technical details of automatic art generation and the interaction between AI and people, as both artists and the audience of art. We introduce two algorithms for generating 3D point clouds and then discuss their actualization as sculpture and incorporation into a holistic art installation. Specifically, the Amalgamated Deep-Dream (ADD) algorithm solves the sparsity problem caused by the naive DeepDream-inspired approach and generates creative and printable point clouds. The Partitioned DeepDream (PDD) algorithm further allows us to explore more diverse 3D object creation by combining point cloud clustering algorithms and ADD. Keywords Partitioned DeepDream, Amalgamated DeepDream, 3D, Point Cloud, Sculpture, Art, Interactive Installation, Creative AI, Machine Learning Introduction Will Artificial Intelligence (AI) replace human artists or will it show us a new perspective into creativity? Our team of artists and AI researchers explore artistic expression using Machine Learning (ML) and design creative ML algorithms to be possible co-creators for human artists. In terms of AIgenerated and AIenabled visual artwork, there has been a good amount of exploration done over the past three years in the 2D image area traditionally belonging to the realm of painting.

We describe ChemBO, a Bayesian Optimization framework for generating and optimizing organic molecules for desired molecular properties. This framework is useful in applications such as drug discovery, where an algorithm recommends new candidate molecules; these molecules first need to be synthesized and then tested for drug-like properties. The algorithm uses the results of past tests to recommend new ones so as to find good molecules efficiently. Most existing data-driven methods for this problem do not account for sample efficiency and/or fail to enforce realistic constraints on synthesizability. In this work, we explore existing kernels for molecules in the literature as well as propose a novel kernel which views a molecule as a graph. In ChemBO, we implement these kernels in a Gaussian process model. Then we explore the chemical space by traversing possible paths of molecular synthesis. Consequently, our approach provides a proposal synthesis path every time it recommends a new molecule to test, a crucial advantage when compared to existing methods. In our experiments, we demonstrate the efficacy of the proposed approach on several molecular optimization problems.

Global routing has been a historically challenging problem in electronic circuit design, where the challenge is to connect a large and arbitrary number of circuit components with wires without violating the design rules for the printed circuit boards or integrated circuits. Similar routing problems also exist in the design of complex hydraulic systems, pipe systems and logistic networks. Existing solutions typically consist of greedy algorithms and hard-coded heuristics. As such, existing approaches suffer from a lack of model flexibility and non-optimum solutions. As an alternative approach, this work presents a deep reinforcement learning method for solving the global routing problem in a simulated environment. At the heart of the proposed method is deep reinforcement learning that enables an agent to produce an optimal policy for routing based on the variety of problems it is presented with leveraging the conjoint optimization mechanism of deep reinforcement learning. Conjoint optimization mechanism is explained and demonstrated in details; the best network structure and the parameters of the learned model are explored. Based on the fine-tuned model, routing solutions and rewards are presented and analyzed. The results indicate that the approach can outperform the benchmark method of a sequential A* method, suggesting a promising potential for deep reinforcement learning for global routing and other routing or path planning problems in general. Another major contribution of this work is the development of a global routing problem sets generator with the ability to generate parameterized global routing problem sets with different size and constraints, enabling evaluation of different routing algorithms and the generation of training datasets for future data-driven routing approaches.

Current state-of-the-art NMT systems use large neural networks that are not only slow to train, but also often require many heuristics and optimization tricks, such as specialized learning rate schedules and large batch sizes. This is undesirable as it requires extensive hyperparameter tuning. In this paper, we propose a curriculum learning framework for NMT that reduces training time, reduces the need for specialized heuristics or large batch sizes, and results in overall better performance. Our framework consists of a principled way of deciding which training samples are shown to the model at different times during training, based on the estimated difficulty of a sample and the current competence of the model. Filtering training samples in this manner prevents the model from getting stuck in bad local optima, making it converge faster and reach a better solution than the common approach of uniformly sampling training examples. Furthermore, the proposed method can be easily applied to existing NMT models by simply modifying their input data pipelines. We show that our framework can help improve the training time and the performance of both recurrent neural network models and Transformers, achieving up to a 70% decrease in training time, while at the same time obtaining accuracy improvements of up to 2.2 BLEU.

Bayesian Optimisation (BO), refers to a suite of techniques for global optimisation of expensive black box functions, which use introspective Bayesian models of the function to efficiently find the optimum. While BO has been applied successfully in many applications, modern optimisation tasks usher in new challenges where conventional methods fail spectacularly. In this work, we present Dragonfly, an open source Python library for scalable and robust BO. Dragonfly incorporates multiple recently developed methods that allow BO to be applied in challenging real world settings; these include better methods for handling higher dimensional domains, methods for handling multi-fidelity evaluations when cheap approximations of an expensive function are available, methods for optimising over structured combinatorial spaces, such as the space of neural network architectures, and methods for handling parallel evaluations. Additionally, we develop new methodological improvements in BO for selecting the Bayesian model, selecting the acquisition function, and optimising over complex domains with different variable types and additional constraints. We compare Dragonfly to a suite of other packages and algorithms for global optimisation and demonstrate that when the above methods are integrated, they enable significant improvements in the performance of BO. The Dragonfly library is available at dragonfly.github.io.

Optimizing an expensive-to-query function is a common task in science and engineering, where it is beneficial to keep the number of queries to a minimum. A popular strategy is Bayesian optimization (BO), which leverages probabilistic models for this task. Most BO today uses Gaussian processes (GPs), or a few other surrogate models. However, there is a broad set of Bayesian modeling techniques that we may want to use to capture complex systems and reduce the number of queries. Probabilistic programs (PPs) are modern tools that allow for flexible model composition, incorporation of prior information, and automatic inference. In this paper, we develop ProBO, a framework for BO using only standard operations common to most PPs. This allows a user to drop in an arbitrary PP implementation and use it directly in BO. To do this, we describe black box versions of popular acquisition functions that can be used in our framework automatically, without model-specific derivation, and show how to optimize these functions. We also introduce a model, which we term the Bayesian Product of Experts, that integrates into ProBO and can be used to combine information from multiple models implemented with different PPs. We show empirical results using multiple PP implementations, and compare against standard BO methods.

We study minimax convergence rates of nonparametric density estimation under a large class of loss functions called ``adversarial losses'', which, besides classical L^p losses, includes maximum mean discrepancy (MMD), Wasserstein distance, and total variation distance. These losses are closely related to the losses encoded by discriminator networks in generative adversarial networks (GANs). In a general framework, we study how the choice of loss and the assumed smoothness of the underlying density together determine the minimax rate. We also discuss implications for training GANs based on deep ReLU networks, and more general connections to learning implicit generative models in a minimax statistical sense.

Bayesian Optimisation (BO) refers to a class of methods for global optimisation of a function f which is only accessible via point evaluations. It is typically used in settings where f is expensive to evaluate. A common use case for BO in machine learning is model selection, where it is not possible to analytically model the generalisation performance of a statistical model, and we resort to noisy and expensive training and validation procedures to choose the best model. Conventional BO methods have focused on Euclidean and categorical domains, which, in the context of model selection, only permits tuning scalar hyper-parameters of machine learning algorithms. However, with the surge of interest in deep learning, there is an increasing demand to tune neural network architectures. In this work, we develop NASBOT, a Gaussian process based BO framework for neural architecture search. To accomplish this, we develop a distance metric in the space of neural network architectures which can be computed efficiently via an optimal transport program. This distance might be of independent interest to the deep learning community as it may find applications outside of BO. We demonstrate that NASBOT outperforms other alternatives for architecture search in several cross validation based model selection tasks on multi-layer perceptrons and convolutional neural networks.