We explicitly solve the nonlinear PDE that is the continuous limit of dynamic programming of \emph{expert prediction problem} in finite horizon setting with $N=4$ experts. The \emph{expert prediction problem} is formulated as a zero sum game between a player and an adversary. By showing that the solution is $\mathcal{C}^2$, we are able to show that the strategies conjectured in arXiv:1409.3040G form an asymptotic Nash equilibrium. We also prove the "Finite vs Geometric regret" conjecture proposed in arXiv:1409.3040G for $N=4$, and we give a stronger conjecture which characterizes the relation between the finite and geometric stopping.

The complex world around us is inherently multimodal and sequential (continuous). Information is scattered across different modalities and requires multiple continuous sensors to be captured. As machine learning leaps towards better generalization to real world, multimodal sequential learning becomes a fundamental research area. Arguably, modeling arbitrarily distributed spatio-temporal dynamics within and across modalities is the biggest challenge in this research area. In this paper, we present a new transformer model, called the Factorized Multimodal Transformer (FMT) for multimodal sequential learning. FMT inherently models the intramodal and intermodal (involving two or more modalities) dynamics within its multimodal input in a factorized manner. The proposed factorization allows for increasing the number of self-attentions to better model the multimodal phenomena at hand; without encountering difficulties during training (e.g. overfitting) even on relatively low-resource setups. All the attention mechanisms within FMT have a full time-domain receptive field which allows them to asynchronously capture long-range multimodal dynamics. In our experiments we focus on datasets that contain the three commonly studied modalities of language, vision and acoustic. We perform a wide range of experiments, spanning across 3 well-studied datasets and 21 distinct labels. FMT shows superior performance over previously proposed models, setting new state of the art in the studied datasets.

A unique challenge for e-commerce recommendation is that customers are often interested in products that are more advanced than their already purchased products, but not reversed. The few existing recommender systems modeling unidirectional sequence output a limited number of categories or continuous variables. To model the ordered sequence, we design the first recommendation system that both embed purchased items with Word2Vec, and model the sequence with stateless LSTM RNN. The click-through rate of this recommender system in production outperforms its solely Word2Vec based predecessor. Developed in 2017, it was perhaps the first published real-world application that makes distributed predictions of a single machine trained Keras model on Spark slave nodes at a scale of more than 0.4 million columns per row.

Frank Noé Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany Gianni De Fabritiis Computational Science Laboratory, Universitat Pompeu Fabra, Barcelona Biomedical Research Park (PRBB), Doctor Aiguader 88, 08003 Barcelona, Spain, and Institucio Catalana de Recerca i Estudis Avanats (ICREA), Passeig Lluis Companys 23, Barcelona 08010, Spain Cecilia Clementi Center for Theoretical Biological Physics, and Department of Chemistry, Rice University, 6100 Main Street, Houston, Texas 77005, United StatesAbstract Many aspects of the study of protein folding and dynamics have been affected by the recent advances in machine learning. Methods for the prediction of protein structures from their sequences are now heavily based on machine learning tools. The way simulations are performed to explore the energy landscape of protein systems is also changing as force-fields are started to be designed by means of machine learning methods. These methods are also used to extract the essential information from large simulation datasets and to enhance the sampling of rare events such as folding/unfolding transitions. While significant challenges still need to be tackled, we expect these methods to play an important role on the study of protein folding and dynamics in the near future. We discuss here the recent advances on all these fronts and the questions that need to be addressed for machine learning approaches to become mainstream in protein simulation.Introduction During the last couple of decades advances in artificial intelligence and machine learning have revolutionized many application areas such as image recognition and language translation. The key of this success has been the design of algorithms that can extract complex patterns and highly nontrivial relationships from large amount of data and abstract this information in the evaluation of new data.

Entity linking is the task of linking mentions of named entities in natural language text, to entities in a curated knowledge-base. This is of significant importance in the biomedical domain, where it could be used to semantically annotate a large volume of clinical records and biomedical literature, to standardized concepts described in an ontology such as Unified Medical Language System (UMLS). We observe that with precise type information, entity disambiguation becomes a straightforward task. However, fine-grained type information is usually not available in biomedical domain. Thus, we propose LATTE, a LATent Type Entity Linking model, that improves entity linking by modeling the latent fine-grained type information about mentions and entities. Unlike previous methods that perform entity linking directly between the mentions and the entities, LATTE jointly does entity disambiguation, and latent fine-grained type learning, without direct supervision. We evaluate our model on two biomedical datasets: MedMentions, a large scale public dataset annotated with UMLS concepts, and a de-identified corpus of dictated doctor's notes that has been annotated with ICD concepts. Extensive experimental evaluation shows our model achieves significant performance improvements over several state-of-the-art techniques.

Monoaural audio source separation is a challenging research area in machine learning. In this area, a mixture containing multiple audio sources is given, and a model is expected to disentangle the mixture into isolated atomic sources. In this paper, we first introduce a challenging new dataset for monoaural source separation called WildMix. WildMix is designed with the goal of extending the boundaries of source separation beyond what previous datasets in this area would allow. It contains diverse in-the-wild recordings from 25 different sound classes, combined with each other using arbitrary composition policies. Source separation often requires modeling long-range dependencies in both temporal and spectral domains. To this end, we introduce a novel trasnformer-based model called Spectro-Temporal Transformer (STT). STT utilizes a specialized encoder, called Spectro-Temporal Encoder (STE). STE highlights temporal and spectral components of sources within a mixture, using a self-attention mechanism. It subsequently disentangles them in a hierarchical manner. In our experiments, STT swiftly outperforms various previous baselines for monoaural source separation on the challenging WildMix dataset.

A BSTRACT Performing controlled experiments on noisy data is essential in thoroughly understanding deep learning across a spectrum of noise levels. Due to the lack of suitable datasets, previous research have only examined deep learning on controlled synthetic noise, and real-world noise has never been systematically studied in a controlled setting. To this end, this paper establishes a benchmark of real-world noisy labels at 10 controlled noise levels. As real-world noise possesses unique properties, to understand the difference, we conduct a large-scale study across a variety of noise levels and types, architectures, methods, and training settings. Our study shows that: (1) Deep Neural Networks (DNNs) generalize much better on real-world noise. We hope our benchmark, as well as our findings, will facilitate deep learning research on noisy data. 1 I NTRODUCTION Y ou take the blue pill you wake up in your bed and believe whatever you want to believe. Y ou take the red pill and I show you how deep the rabbit hole goes. Remember, all I'm offering is the truth. Morpheus (The Matrix 1999) Deep Neural Networks (DNNs) trained on noisy data demonstrate intriguing properties. For example, DNNs are capable of memorizing completely random training labels but generalize poorly on clean test data Zhang et al. (2017). When trained with stochastic gradient descent, DNNs learn patterns first before memorizing the label noise Arpit et al. (2017). These findings inspired recent research on noisy data. As training data are usually noisy, the fact that DNNs are able to memorize the noisy labels highlights the importance of deep learning research on noisy data. To study DNNs on noisy data, previous work often performs controlled experiments by injecting a series of synthetic noises into a well-annotated dataset. The noise level p may vary in the range of 0%- 100%, where p 0% is the clean dataset whereas p 100% represents the dataset of zero correct labels.

Membership inference attacks seek to infer the membership of individual training instances of a privately trained model. This paper presents a membership privacy analysis and evaluation system, called MPLens, with three unique contributions. First, through MPLens, we demonstrate how membership inference attack methods can be leveraged in adversarial machine learning. Second, through MPLens, we highlight how the vulnerability of pre-trained models under membership inference attack is not uniform across all classes, particularly when the training data itself is skewed. We show that risk from membership inference attacks is routinely increased when models use skewed training data. Finally, we investigate the effectiveness of differential privacy as a mitigation technique against membership inference attacks. We discuss the trade-offs of implementing such a mitigation strategy with respect to the model complexity, the learning task complexity, the dataset complexity and the privacy parameter settings. Our empirical results reveal that (1) minority groups within skewed datasets display increased risk for membership inference and (2) differential privacy presents many challenging trade-offs as a mitigation technique to membership inference risk.

Gibbs sampling is a Markov chain Monte Carlo method that is often used for learning and inference on graphical models. Minibatching, in which a small random subset of the graph is used at each iteration, can help make Gibbs sampling scale to large graphical models by reducing its computational cost. In this paper, we propose a new auxiliary-variable minibatched Gibbs sampling method, {\it Poisson-minibatching Gibbs}, which both produces unbiased samples and has a theoretical guarantee on its convergence rate. In comparison to previous minibatched Gibbs algorithms, Poisson-minibatching Gibbs supports fast sampling from continuous state spaces and avoids the need for a Metropolis-Hastings correction on discrete state spaces. We demonstrate the effectiveness of our method on multiple applications and in comparison with both plain Gibbs and previous minibatched methods.

Batch Normalization (BN) is a highly successful and widely used batch dependent training method. Its use of mini-batch statistics to normalize the activations introduces dependence between samples, which can hurt the training if the mini-batch size is too small, or if the samples are correlated. Several alternatives, such as Batch Renormalization and Group Normalization (GN), have been proposed to address these issues. However, they either do not match the performance of BN for large batches, or still exhibit degradation in performance for smaller batches, or introduce artificial constraints on the model architecture. In this paper we propose the Filter Response Normalization (FRN) layer, a novel combination of a normalization and an activation function, that can be used as a drop-in replacement for other normalizations and activations. Our method operates on each activation map of each batch sample independently, eliminating the dependency on other batch samples or channels of the same sample. Our method outperforms BN and all alternatives in a variety of settings for all batch sizes. FRN layer performs $\approx 0.7-1.0\%$ better on top-1 validation accuracy than BN with large mini-batch sizes on Imagenet classification on InceptionV3 and ResnetV2-50 architectures. Further, it performs $>1\%$ better than GN on the same problem in the small mini-batch size regime. For object detection problem on COCO dataset, FRN layer outperforms all other methods by at least $0.3-0.5\%$ in all batch size regimes.