This paper studies clustering for possibly high dimensional data (\emph{e.g.} images, time series, gene expression data, and many other settings), and rephrase it as low rank matrix estimation in the PAC-Bayesian framework. Our approach leverages the well known Burer-Monteiro factorisation strategy from large scale optimisation, in the context of low rank estimation. Moreover, our Burer-Monteiro factors are shown to lie on a Stiefel manifold. We propose a new generalized Bayesian estimator for this problem and prove novel prediction bounds for clustering. We also devise a componentwise Langevin sampler on the Stiefel manifold to compute this estimator.
Ali Taylan Cemgil, Mehmet Burak Kurutmaz, Sinan Yildirim, Melih Barsbey, Umut Simsekli
2019-03-11
We introduce a dynamic generative model, Bayesian allocation model (BAM), which establishes explicit connections between nonnegative tensor factorization (NTF), graphical models of discrete probability distributions and their Bayesian extensions, and the topic models such as the latent Dirichlet allocation. BAM is based on a Poisson process, whose events are marked by using a Bayesian network, where the conditional probability tables of this network are then integrated out analytically. We show that the resulting marginal process turns out to be a Polya urn, an integer valued self-reinforcing process. This urn processes, which we name a Polya-Bayes process, obey certain conditional independence properties that provide further insight about the nature of NTF. These insights also let us develop space efficient simulation algorithms that respect the potential sparsity of data: we propose a class of sequential importance sampling algorithms for computing NTF and approximating their marginal likelihood, which would be useful for model selection. The resulting methods can also be viewed as a model scoring method for topic models and discrete Bayesian networks with hidden variables. The new algorithms have favourable properties in the sparse data regime when contrasted with variational algorithms that become more accurate when the total sum of the elements of the observed tensor goes to infinity. We illustrate the performance on several examples and numerically study the behaviour of the algorithms for various data regimes.
We introduce Continual Learning via Neural Pruning (CLNP), a new method aimed at lifelong learning in fixed capacity models based on neuronal model sparsification. In this method, subsequent tasks are trained using the inactive neurons and filters of the sparsified network and cause zero deterioration to the performance of previous tasks. In order to deal with the possible compromise between model sparsity and performance, we formalize and incorporate the concept of graceful forgetting: the idea that it is preferable to suffer a small amount of forgetting in a controlled manner if it helps regain network capacity and prevents uncontrolled loss of performance during the training of future tasks. CLNP also provides simple continual learning diagnostic tools in terms of the number of free neurons left for the training of future tasks as well as the number of neurons that are being reused. In particular, we see in experiments that CLNP verifies and automatically takes advantage of the fact that the features of earlier layers are more transferable. We show empirically that CLNP leads to significantly improved results over current weight elasticity based methods.
Following the recent work on capacity allocation, we formulate the conjecture that the shattering problem in deep neural networks can only be avoided if the capacity propagation through layers has a non-degenerate continuous limit when the number of layers tends to infinity. This allows us to study a number of commonly used architectures and determine which scaling relations should be enforced in practice as the number of layers grows large. In particular, we recover the conditions of Xavier initialization in the multi-channel case, and we find that weights and biases should be scaled down as the inverse square root of the number of layers for deep residual networks and as the inverse square root of the desired memory length for recurrent networks.
We propose that intelligently combining models from the domains of Artificial Intelligence or Machine Learning with Physical and Expert models will yield a more "trustworthy" model than any one model from a single domain, given a complex and narrow enough problem. Based on mean-variance portfolio theory and bias-variance trade-off analysis, we prove combining models from various domains produces a model that has lower risk, increasing user trust. We call such combined models - physics enhanced artificial intelligence (PEAI), and suggest use cases for PEAI.
Unobserved confounding is a central barrier to drawing causal inferences from observational data. Several authors have recently proposed that this barrier can be overcome in the case where one attempts to infer the effects of several variables simultaneously. In this paper, we present two simple, analytical counterexamples that challenge the general claims that are central to these approaches. In addition, we show that nonparametric identification is impossible in this setting. We discuss practical implications, and suggest alternatives to the methods that have been proposed so far in this line of work: using proxy variables and shifting focus to sensitivity analysis.
We introduce the {\it diffusion -means} clustering method on Riemannian submanifolds, which maximizes the within-cluster connectedness based on the diffusion distance. The diffusion -means constructs a random walk on the similarity graph with vertices as data points randomly sampled on the manifolds and edges as similarities given by a kernel that captures the local geometry of manifolds. Thus the diffusion -means is a multi-scale clustering tool that is suitable for data with non-linear and non-Euclidean geometric features in mixed dimensions. Given the number of clusters, we propose a polynomial-time convex relaxation algorithm via the semidefinite programming (SDP) to solve the diffusion -means. In addition, we also propose a nuclear norm (i.e., trace norm) regularized SDP that is adaptive to the number of clusters. In both cases, we show that exact recovery of the SDPs for diffusion -means can be achieved under suitable between-cluster separability and within-cluster connectedness of the submanifolds, which together quantify the hardness of the manifold clustering problem. We further propose the {\it localized diffusion -means} by using the local adaptive bandwidth estimated from the nearest neighbors. We show that exact recovery of the localized diffusion -means is fully adaptive to the local probability density and geometric structures of the underlying submanifolds.
Leni K. Le Goff, Oussama Yaakoubi, Alexandre Coninx, Stephane Doncieux
2019-03-11
Robots need to understand their environment to perform their task. If it is possible to pre-program a visual scene analysis process in closed environments, robots operating in an open environment would benefit from the ability to learn it through their interaction with their environment. This ability furthermore opens the way to the acquisition of affordances maps in which the action capabilities of the robot structure its visual scene understanding. We propose an approach to build such affordances maps by relying on an interactive perception approach and an online classification. In the proposed formalization of affordances, actions and effects are related to visual features, not objects, and they can be combined. We have tested the approach on three action primitives and on a real PR2 robot.
Pravendra Singh, Pratik Mazumder, Vinay P. Namboodiri
2019-03-11
Convolution Neural Networks (CNN) have been extremely successful in solving intensive computer vision tasks. The convolutional filters used in CNNs have played a major role in this success, by extracting useful features from the inputs. Recently researchers have tried to boost the performance of CNNs by re-calibrating the feature maps produced by these filters, e.g., Squeeze-and-Excitation Networks (SENets). These approaches have achieved better performance by \textit{Exciting} up the important channels or feature maps while diminishing the rest. However, in the process, architectural complexity has increased. We propose an architectural block that introduces much lower complexity than the existing methods of CNN performance boosting while performing significantly better than them. We carry out experiments on the CIFAR, ImageNet and MS-COCO datasets, and show that the proposed block can challenge the state-of-the-art results. Our method boosts the ResNet-50 architecture to perform comparably to the ResNet-152 architecture, which is a three times deeper network, on classification. We also show experimentally that our method is not limited to classification but also generalizes well to other tasks such as object detection.
Daniel C. Elton, Zois Boukouvalas, Mark D. Fuge, Peter W. Chung
2019-03-11
In the space of only a few years, deep generative modeling has revolutionized how we think of artificial creativity, yielding autonomous systems which produce original images, music, and text. Inspired by these successes, researchers are now applying deep generative modeling techniques to the generation and optimization of molecules - in our review we found 45 papers on the subject published in the past two years. These works point to a future where such systems will be used to generate lead molecules, greatly reducing resources spent downstream synthesizing and characterizing bad leads in the lab. In this review we survey the increasingly complex landscape of models and representation schemes that have been proposed. The four classes of techniques we describe are recursive neural networks, autoencoders, generative adversarial networks, and reinforcement learning. After first discussing some of the mathematical fundamentals of each technique, we draw high level connections and comparisons with other techniques and expose the pros and cons of each. Several important high level themes emerge as a result of this work, including the shift away from the SMILES string representation of molecules towards more sophisticated representations such as graph grammars and 3D representations, the importance of reward function design, the need for better standards for benchmarking and testing, and the benefits of adversarial training and reinforcement learning over maximum likelihood based training.
