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Publications
Expressiveness and Learning of Hidden Quantum Markov Models
Extending classical probabilistic reasoning using the quantum mechanical view of probability has been of recent interest, particularly in th… (voir plus)e development of hidden quantum Markov models (HQMMs) to model stochastic processes. However, there has been little progress in characterizing the expressiveness of such models and learning them from data. We tackle these problems by showing that HQMMs are a special subclass of the general class of observable operator models (OOMs) that do not suffer from the \emph{negative probability problem} by design. We also provide a feasible retraction-based learning algorithm for HQMMs using constrained gradient descent on the Stiefel manifold of model parameters. We demonstrate that this approach is faster and scales to larger models than previous learning algorithms.
Not all patients who need kidney transplant can find a donor with compatible characteristics. Kidney exchange programs (KEPs) seek to match … (voir plus)such incompatible patient-donor pairs together, usually with the objective of maximizing the total number of transplants. We propose a randomized policy for selecting an optimal solution in which patients’ equity of opportunity to receive a transplant is promoted. Our approach gives rise to the problem of enumerating all optimal solutions, which we tackle using a hybrid of constraint programming and linear programming. We empirically demonstrate the advantages of our proposed method over the common practice of using the first optimal solution obtained by a solver.
Fast and Furious Convergence: Stochastic Second Order Methods under Interpolation
We consider stochastic second-order methods for minimizing smooth and strongly-convex functions under an interpolation condition satisfied b… (voir plus)y over-parameterized models. Under this condition, we show that the regularized subsampled Newton method (R-SSN) achieves global linear convergence with an adaptive step-size and a constant batch-size. By growing the batch size for both the subsampled gradient and Hessian, we show that R-SSN can converge at a quadratic rate in a local neighbourhood of the solution. We also show that R-SSN attains local linear convergence for the family of self-concordant functions. Furthermore, we analyze stochastic BFGS algorithms in the interpolation setting and prove their global linear convergence. We empirically evaluate stochastic L-BFGS and a "Hessian-free" implementation of R-SSN for binary classification on synthetic, linearly-separable datasets and real datasets under a kernel mapping. Our experimental results demonstrate the fast convergence of these methods, both in terms of the number of iterations and wall-clock time.
We address the problem of credit assignment in reinforcement learning and explore fundamental questions regarding the way in which an agent … (voir plus)can best use additional computation to propagate new information, by planning with internal models of the world to improve its predictions. Particularly, we work to understand the gains and peculiarities of planning employed as forethought via forward models or as hindsight operating with backward models. We establish the relative merits, limitations and complementary properties of both planning mechanisms in carefully constructed scenarios. Further, we investigate the best use of models in planning, primarily focusing on the selection of states in which predictions should be (re)-evaluated. Lastly, we discuss the issue of model estimation and highlight a spectrum of methods that stretch from explicit environment-dynamics predictors to more abstract planner-aware models.
We advocate the use of a notion of entropy that reflects the relative abundances of the symbols in an alphabet, as well as the similarities … (voir plus)between them. This concept was originally introduced in theoretical ecology to study the diversity of ecosystems. Based on this notion of entropy, we introduce geometry-aware counterparts for several concepts and theorems in information theory. Notably, our proposed divergence exhibits performance on par with state-of-the-art methods based on the Wasserstein distance, but enjoys a closed-form expression that can be computed efficiently. We demonstrate the versatility of our method via experiments on a broad range of domains: training generative models, computing image barycenters, approximating empirical measures and counting modes.
We present GraphMix , a regularized training scheme for Graph Neural Network based semi-supervised object classification, leveraging the re… (voir plus)cent advances in the regularization of classical deep neural networks. Specifically, we pro-pose a unified approach in which we train a fully-connected network jointly with the graph neural network via parameter sharing, interpolation-based regularization and self-predicted-targets. Our proposed method is architecture agnostic in the sense that it can be applied to any variant of graph neural networks which applies a parametric transformation to the features of the graph nodes. Despite its simplicity, with GraphMix we can consistently improve results and achieve or closely match state-of-the-art performance using even simpler architectures such as Graph Convolutional Networks, across three established graph benchmarks: Cora, Citeseer and Pubmed citation network datasets, as well as three newly proposed datasets :Cora-Full, Co-author-CS and Co-author-Physics.
We study the implicit regularization of optimization methods for linear models interpolating the training data in the under-parametrized and… (voir plus) over-parametrized regimes. For over-parameterized linear regression, where there are infinitely many interpolating solutions, different optimization methods can converge to solutions with varying generalization performance. In this setting, we show that projections onto linear spans can be used to move between solutions. Furthermore, via a simple reparameterization, we can ensure that an arbitrary optimizer converges to the minimum (cid:96) 2 -norm solution with favourable generalization properties. For under-parameterized linear clas-sification, optimizers can converge to different decision boundaries separating the data. We prove that for any such classifier, there exists a family of quadratic norms (cid:107)·(cid:107) P such that the classifier’s direction is the same as that of the maximum P -margin solution. We argue that analyzing convergence to the standard maximum (cid:96) 2 -margin is arbitrary and show that minimizing the norm induced by the data can result in better generalization. We validate our theoretical results via experiments on synthetic and real datasets.
Investigating the Barriers to Physician Adoption of an Artificial Intelligence- Based Decision Support System in Emergency Care: An Interpretative Qualitative Study.
In this work, we perform authorship attri-bution on a new dataset of German news articles. We seek to classify over 3,700 articles to their … (voir plus)five corresponding authors, using four conventional machine learning approaches (na¨ıve Bayes, logistic regression, SVM and kNN) and a convolutional neural network. We analyze the effect of character and word n-grams on the prediction accuracy, as well as the influence of stop words, punctuation, numbers, and lowercasing when preprocessing raw text. The experiments show that higher order character n-grams (n = 5,6) perform better than lower orders and word n-grams slightly outperform those with characters. Combining both in fusion models further improves results up to 92% for SVM. A multilayer convolutional structure allows the CNN to achieve 90.5% accuracy. We found stop words and punctuation to be important features for author identification; removing them leads to a measurable decrease in performance. Finally, we evaluate the topic dependency of the algorithms by gradually replacing named entities, nouns, verbs and eventually all to-kens in the dataset according to their POS-tags.
Investigating the interconnections between human, technology and context in the implementation of a AI-based health information technology: a dynamic technological frame perspective
