This paper presents the machine learning architecture of the Snips Voice Platform, a software solution to perform Spoken Language Understanding on microprocessors typical of IoT devices. The embedded inference is fast and accurate while enforcing privacy by design, as no personal user data is ever collected. Focusing on Automatic Speech Recognition and Natural Language Understanding, we detail our approach to training high-performance Machine Learning models that are small enough to run in real-time on small devices. Additionally, we describe a data generation procedure that provides sufficient, high-quality training data without compromising user privacy.1 https://www.voicebot.ai/2018/03/07/new-voicebot-report-says-nearly-20-u-sadults-smart-speakers/ 2 In French: https://www.cnil.fr/fr/enceintes-intelligentes-des-assistants-vocauxconnectes-votre-vie-privee 3 https://www.eugdpr.org/

Epidemics are often modeled using non-linear dynamical systems observed through partial and noisy data. In this paper, we consider stochastic extensions in order to capture unknown influences (changing behaviors, public interventions, seasonal effects, etc.). These models assign diffusion processes to the time-varying parameters, and our inferential procedure is based on a suitably adjusted adaptive particle Markov chain Monte Carlo algorithm. The performance of the proposed computational methods is validated on simulated data and the adopted model is applied to the 2009 H1N1 pandemic in England. In addition to estimating the effective contact rate trajectories, the methodology is applied in real time to provide evidence in related public health decisions. Diffusion-driven susceptible exposed infected retired-type models with age structure are also introduced.

The spread of disease through human populations is complex. The characteristics of disease propagation evolve with time, as a result of a multitude of environmental and anthropic factors, this non-stationarity is a key factor in this huge complexity. In the absence of appropriate external data sources, to correctly describe the disease propagation, we explore a flexible approach, based on stochastic models for the disease dynamics, and on diffusion processes for the parameter dynamics. Using such a diffusion process has the advantage of not requiring a specific mathematical function for the parameter dynamics. Coupled with particle MCMC, this approach allows us to reconstruct the time evolution of some key parameters (average transmission rate for instance). Thus, by capturing the time-varying nature of the different mechanisms involved in disease propagation, the epidemic can be described. Firstly we demonstrate the efficiency of this methodology on a toy model, where the parameters and the observation process are known. Applied then to real datasets, our methodology is able, based solely on simple stochastic models, to reconstruct complex epidemics, such as flu or dengue, over long time periods. Hence we demonstrate that time-varying parameters can improve the accuracy of model performances, and we suggest that our methodology can be used as a first step towards a better understanding of a complex epidemic, in situation where data is limited and/or uncertain.

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Original citation:Beskos, A., Dureau, J. and Kalogeropoulos, K. (2015) Bayesian inference for partially observed stochastic differential equations driven by fractional Brownian motion. Biometrika, 102 (4 Houghton Street, London WC2A 2AE, U.K. k.kalogeropoulos@lse.ac.uk SUMMARY We consider continuous-time diffusion models driven by fractional Brownian motion. Observations are assumed to possess a non-trivial likelihood given the latent path. Due to the nonMarkovianity and high dimensionality of the latent paths, estimating posterior expectations is computationally challenging. We present a reparameterization framework based on the Davies and Harte method for sampling stationary Gaussian processes and use it to construct a Markov chain Monte Carlo algorithm that allows computationally efficient Bayesian inference. The algorithm is based on a version of hybrid Monte Carlo that delivers increased efficiency when applied on the high-dimensional latent variables arising in this context. We specify the methodology on a stochastic volatility model, allowing for memory in the volatility increments through a fractional specification. The methodology is illustrated on simulated data and on the S&P500/VIX time series the posterior distribution favours values of the Hurst parameter, smaller than 1/2, pointing towards medium range dependence.Some key words: Bayesian inference; Davies and Harte algorithm; fractional Brownian motion; hybrid Monte Carlo.