This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent's iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly.

We use persistent homology along with the eigenfunctions of the Laplacian to study similarity amongst triangulated 2-manifolds. Our method relies on studying the lower-star filtration induced by the eigenfunctions of the Laplacian. This gives us a shape descriptor that inherits the rich information encoded in the eigenfunctions of the Laplacian. Moreover, the similarity between these descriptors can be easily computed using tools that are readily available in Topological Data Analysis. We provide experiments to illustrate the effectiveness of the proposed method.

Multi-label classification is an approach which allows a datapoint to be labelled with more than one class at the same time. A common but trivial approach is to train individual binary classifiers per label, but the performance can be improved by considering associations within the labels. Like with any machine learning algorithm, hyperparameter tuning is important to train a good multi-label classifier model. The task of selecting the best hyperparameter settings for an algorithm is an optimisation problem. Very limited work has been done on automatic hyperparameter tuning and AutoML in the multi-label domain. This paper attempts to fill this gap by proposing a neural network algorithm, CascadeML, to train multi-label neural network based on cascade neural networks. This method requires minimal or no hyperparameter tuning and also considers pairwise label associations. The cascade algorithm grows the network architecture incrementally in a two phase process as it learns the weights using adaptive first order gradient algorithm, therefore omitting the requirement of preselecting the number of hidden layers, nodes and the learning rate. The method was tested on 10 multi-label datasets and compared with other multi-label classification algorithms. Results show that CascadeML performs very well without hyperparameter tuning.

Memory is increasingly often the bottleneck when training neural network models. Despite this, techniques to lower the overall memory requirements of training have been less widely studied compared to the extensive literature on reducing the memory requirements of inference. In this paper we study a fundamental question: How much memory is actually needed to train a neural network? To answer this question, we profile the overall memory usage of training on two representative deep learning benchmarks -- the WideResNet model for image classification and the DynamicConv Transformer model for machine translation -- and comprehensively evaluate four standard techniques for reducing the training memory requirements: (1) imposing sparsity on the model, (2) using low precision, (3) microbatching, and (4) gradient checkpointing. We explore how each of these techniques in isolation affects both the peak memory usage of training and the quality of the end model, and explore the memory, accuracy, and computation tradeoffs incurred when combining these techniques. Using appropriate combinations of these techniques, we show that it is possible to the reduce the memory required to train a WideResNet-28-2 on CIFAR-10 by up to 60.7x with a 0.4% loss in accuracy, and reduce the memory required to train a DynamicConv model on IWSLT'14 German to English translation by up to 8.7x with a BLEU score drop of 0.15.

Large scale machine learning (ML) systems such as the Alexa automatic speech recognition (ASR) system continue to improve with increasing amounts of manually transcribed training data. Instead of scaling manual transcription to impractical levels, we utilize semi-supervised learning (SSL) to learn acoustic models (AM) from the vast firehose of untranscribed audio data. Learning an AM from 1 Million hours of audio presents unique ML and system design challenges. We present the design and evaluation of a highly scalable and resource efficient SSL system for AM. Employing the student/teacher learning paradigm, we focus on the student learning subsystem: a scalable and robust data pipeline that generates features and targets from raw audio, and an efficient model pipeline, including the distributed trainer, that builds a student model. Our evaluations show that, even without extensive hyper-parameter tuning, we obtain relative accuracy improvements in the 10 to 20$\%$ range, with higher gains in noisier conditions. The end-to-end processing time of this SSL system was 12 days, and several components in this system can trivially scale linearly with more compute resources.

In this paper, we propose an extension to an existing algorithm (instance-MIR) which tackles the multiple instance regression (MIR) problem, also known as distribution regression. The MIR setting arises when the data is a collection of bags, where each bag consists of several instances which correspond to the same and unique real-valued label. The goal of a MIR algorithm is to find a mapping from the instances of an unseen bag to its target value. The instance-MIR algorithm treats all the instances separately and maps each instance to a label. The final bag label is then taken as the mean or the median of the predictions for that given bag. While it is conceptually simple, taking a single statistic to summarize the distribution of the labels in each bag is a limitation. In spite of this performance bottleneck, the instance-MIR algorithm has been shown to be competitive when compared to the current state-of-the-art methods. We address the aforementioned issue by computing the kernel mean embeddings of the distributions of the predicted labels, for each bag, and learn a regressor from these embeddings to the bag label. We test our algorithm (instance-kme-MIR) on five real world datasets and obtain better results than the baseline instance-MIR across all the datasets, while achieving state-of-the-art results on two of the datasets.

We present an algorithm for learning a latent variable generative model via generative adversarial learning where the canonical uniform noise input is replaced by samples from a graphical model. This graphical model is learned by a Boltzmann machine which learns low-dimensional feature representation of data extracted by the discriminator. A quantum annealer, the D-Wave 2000Q, is used to sample from this model. This algorithm joins a growing family of algorithms that use a quantum annealing subroutine in deep learning, and provides a framework to test the advantages of quantum-assisted learning in GANs. Fully connected, symmetric bipartite and Chimera graph topologies are compared on a reduced stochastically binarized MNIST dataset, for both classical and quantum annealing sampling methods. The quantum-assisted associative adversarial network successfully learns a generative model of the MNIST dataset for all topologies, and is also applied to the LSUN dataset bedrooms class for the Chimera topology. Evaluated using the Fr\'{e}chet inception distance and inception score, the quantum and classical versions of the algorithm are found to have equivalent performance for learning an implicit generative model of the MNIST dataset.

Multimodal learning has been lacking principled ways of combining information from different modalities and learning a low-dimensional manifold of meaningful representations. We study multimodal learning and sensor fusion from a latent variable perspective. We first present a regularized recurrent attention filter for sensor fusion. This algorithm can dynamically combine information from different types of sensors in a sequential decision making task. Each sensor is bonded with a modular neural network to maximize utility of its own information. A gating modular neural network dynamically generates a set of mixing weights for outputs from sensor networks by balancing utility of all sensors' information. We design a co-learning mechanism to encourage co-adaption and independent learning of each sensor at the same time, and propose a regularization based co-learning method. In the second part, we focus on recovering the manifold of latent representation. We propose a co-learning approach using probabilistic graphical model which imposes a structural prior on the generative model: multimodal variational RNN (MVRNN) model, and derive a variational lower bound for its objective functions. In the third part, we extend the siamese structure to sensor fusion for robust acoustic event detection. We perform experiments to investigate the latent representations that are extracted; works will be done in the following months. Our experiments show that the recurrent attention filter can dynamically combine different sensor inputs according to the information carried in the inputs. We consider MVRNN can identify latent representations that are useful for many downstream tasks such as speech synthesis, activity recognition, and control and planning. Both algorithms are general frameworks which can be applied to other tasks where different types of sensors are jointly used for decision making.

In the last few years, there have been many methodological and theoretical advances in the random forests approach. Some methodological developments and extensions include case-specific random forests [19], multivariate random forests [16], quantile regression forests [13], random survival forests [11], enriched random forests for microarry data [1] and predictor augmentation in random forests [18] among others. For theoretical developments, the statistical and asymptotic properties of random forests have been intensively investigated. Advances have been made in the areas such as consistency [2] [15], variable selection [8] and the construction of confidence intervals [17]. Although RF methodology has proven itself to be a reliable predictive approach in many application areas [3][10], there are some cases where random forests may suffer. First, as a fully nonparametric predictive algorithm, random forests may not efficiently incorporate known relationships between the response and the predictors. Second, random forests may fail in extrapolation problems where predictions are required at points out of the domain of the training dataset. For regression problems, a random forest prediction is an average of the predictions produced by the trees in the forest.

In this paper, we propose a semi-supervised deep learning method for detecting the specific types of reads that impede the de novo genome assembly process. Instead of dealing directly with sequenced reads, we analyze their coverage graphs converted to 1D-signals. We noticed that specific signal patterns occur in each relevant class of reads. Semi-supervised approach is chosen because manually labelling the data is a very slow and tedious process, so our goal was to facilitate the assembly process with as little labeled data as possible. We tested two models to learn patterns in the coverage graphs: M1 M2 and semi-GAN. We evaluated the performance of each model based on a manually labeled dataset that comprises various reads from multiple reference genomes with respect to the number of labeled examples that were used during the training process. In addition, we embedded our detection in the assembly process which improved the quality of assemblies.