We investigate the use of alternative divergences to Kullback-Leibler (KL) in variational inference(VI), based on the Variational Dropout \cite{kingma2015}. Stochastic gradient variational Bayes (SGVB) \cite{aevb} is a general framework for estimating the evidence lower bound (ELBO) in Variational Bayes. In this work, we extend the SGVB estimator with using Alpha-Divergences, which are alternative to divergences to VI' KL objective. The Gaussian dropout can be seen as a local reparametrization trick of the SGVB objective. We extend the Variational Dropout to use alpha divergences for variational inference. Our results compare $\alpha$-divergence variational dropout with standard variational dropout with correlated and uncorrelated weight noise. We show that the $\alpha$-divergence with $\alpha \rightarrow 1$ (or KL divergence) is still a good measure for use in variational inference, in spite of the efficient use of Alpha-divergences for Dropout VI \cite{Li17}. $\alpha \rightarrow 1$ can yield the lowest training error, and optimizes a good lower bound for the evidence lower bound (ELBO) among all values of the parameter $\alpha \in [0,\infty)$.

When used as a surrogate objective for maximum likelihood estimation in latent variable models, the evidence lower bound (ELBO) produces state-of-the-art results. Inspired by this, we consider the extension of the ELBO to a family of lower bounds defined by a particle filter's estimator of the marginal likelihood, the filtering variational objectives (FIVOs). FIVOs take the same arguments as the ELBO, but can exploit a model's sequential structure to form tighter bounds. We present results that relate the tightness of FIVO's bound to the variance of the particle filter's estimator by considering the generic case of bounds defined as log-transformed likelihood estimators. Experimentally, we show that training with FIVO results in substantial improvements over training the same model architecture with the ELBO on sequential data.

Epileptic seizure activity shows complicated dynamics in both space and time. To understand the evolution and propagation of seizures spatially extended sets of data need to be analysed. We have previously described an efficient filtering scheme using variational Laplace that can be used in the Dynamic Causal Modelling (DCM) framework [Friston, 2003] to estimate the temporal dynamics of seizures recorded using either invasive or non-invasive electrical recordings (EEG/ECoG). Spatiotemporal dynamics are modelled using a partial differential equation -- in contrast to the ordinary differential equation used in our previous work on temporal estimation of seizure dynamics [Cooray, 2016]. We provide the requisite theoretical background for the method and test the ensuing scheme on simulated seizure activity data and empirical invasive ECoG data. The method provides a framework to assimilate the spatial and temporal dynamics of seizure activity, an aspect of great physiological and clinical importance.

Sparse pseudo-point approximations for Gaussian process (GP) models provide a suite of methods that support deployment of GPs in the large data regime and enable analytic intractabilities to be sidestepped. However, the field lacks a principled method to handle streaming data in which both the posterior distribution over function values and the hyperparameter estimates are updated in an online fashion. The small number of existing approaches either use suboptimal hand-crafted heuristics for hyperparameter learning, or suffer from catastrophic forgetting or slow updating when new data arrive. This paper develops a new principled framework for deploying Gaussian process probabilistic models in the streaming setting, providing methods for learning hyperparameters and optimising pseudo-input locations. The proposed framework is assessed using synthetic and real-world datasets.

We search for digital biomarkers from Parkinson's Disease by observing approximate repetitive patterns matching hypothesized step and stride periodic cycles. These observations were modeled as a cycle of hidden states with randomness allowing deviation from a canonical pattern of transitions and emissions, under the hypothesis that the averaged features of hidden states would serve to informatively characterize classes of patients/controls. We propose a Hidden Semi-Markov Model (HSMM), a latent-state model, emitting 3D-acceleration vectors. Transitions and emissions are inferred from data. We fit separate models per unique device and training label. Hidden Markov Models (HMM) force geometric distributions of the duration spent at each state before transition to a new state. Instead, our HSMM allows us to specify the distribution of state duration. This modified version is more effective because we are interested more in each state's duration than the sequence of distinct states, allowing inclusion of these durations the feature vector.

Many efforts have been made to use various forms of domain knowledge in malware detection. Currently there exist two common approaches to malware detection without domain knowledge, namely byte n-grams and strings. In this work we explore the feasibility of applying neural networks to malware detection and feature learning. We do this by restricting ourselves to a minimal amount of domain knowledge in order to extract a portion of the Portable Executable (PE) header. By doing this we show that neural networks can learn from raw bytes without explicit feature construction, and perform even better than a domain knowledge approach that parses the PE header into explicit features.

Bayesian neural networks (BNNs) with latent variables are probabilistic models which can automatically identify complex stochastic patterns in the data. We describe and study in these models a decomposition of predictive uncertainty into its epistemic and aleatoric components. First, we show how such a decomposition arises naturally in a Bayesian active learning scenario by following an information theoretic approach. Second, we use a similar decomposition to develop a novel risk sensitive objective for safe reinforcement learning (RL). This objective minimizes the effect of model bias in environments whose stochastic dynamics are described by BNNs with latent variables. Our experiments illustrate the usefulness of the resulting decomposition in active learning and safe RL settings.

Depending on the algorithm/model that generates this dataset metrics present in the dataset will vary. Here is a list of metrics based on the model: Linear Regression, CART numeric, Elastic Net Linear: R-Square, R-Square Adjusted, Mean Absolute Error(MAE), Mean Squared Error(MSE), Relative Absolute Error(RAE), Related Squared Error(RSE), Root Mean Squared Error(RMSE) CART(Classification And Regression Trees), Naive Bayes Classification, Neural Network, Support Vector Machine(SVM), Random Forest, Logistic Regression: Now you know what the Related datasets are and how they can be useful for fine tuning your Machine Learning model or for comparing two different models. .

Predicting the completion time of business process instances would be a very helpful aid when managing processes under service level agreement constraints. The ability to know in advance the trend of running process instances would allow business managers to react in time, in order to prevent delays or undesirable situations. However, making such accurate forecasts is not easy: many factors may influence the required time to complete a process instance. In this paper, we propose an approach based on deep Recurrent Neural Networks (specifically LSTMs) that is able to exploit arbitrary information associated to single events, in order to produce an as-accurate-as-possible prediction of the completion time of running instances. Experiments on real-world datasets confirm the quality of our proposal.

We consider the problem of predicting the next observation given a sequence of past observations, and consider the extent to which accurate prediction requires complex algorithms that explicitly leverage long-range dependencies. Perhaps surprisingly, our positive results show that for a broad class of sequences, there is an algorithm that predicts well on average, and bases its predictions only on the most recent few observation together with a set of simple summary statistics of the past observations. Specifically, we show that for any distribution over observations, if the mutual information between past observations and future observations is upper bounded by $I$, then a simple Markov model over the most recent $I/\epsilon$ observations obtains expected KL error $\epsilon$---and hence $\ell_1$ error $\sqrt{\epsilon}$---with respect to the optimal predictor that has access to the entire past and knows the data generating distribution. For a Hidden Markov Model with $n$ hidden states, $I$ is bounded by $\log n$, a quantity that does not depend on the mixing time, and we show that the trivial prediction algorithm based on the empirical frequencies of length $O(\log n/\epsilon)$ windows of observations achieves this error, provided the length of the sequence is $d^{\Omega(\log n/\epsilon)}$, where $d$ is the size of the observation alphabet. We also establish that this result cannot be improved upon, even for the class of HMMs, in the following two senses: First, for HMMs with $n$ hidden states, a window length of $\log n/\epsilon$ is information-theoretically necessary to achieve expected $\ell_1$ error $\sqrt{\epsilon}$. Second, the $d^{\Theta(\log n/\epsilon)}$ samples required to estimate the Markov model for an observation alphabet of size $d$ is necessary for any computationally tractable learning algorithm, assuming the hardness of strongly refuting a certain class of CSPs.