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Abstract

We propose an online learning algorithm for training a logistic regression model on nonstationary classification problems. The nonstationarity is captured by modelling the weights in a logistic regression classifier as evolving according to a first order Markov process. The weights are updated using the extended Kalman filter formalism and nonstationarities are tracked by inferring a time-varying state noise variance parameter. We describe an algorithm for doing this based on maximising the evidence of updated predictions. The algorithm is illustrated on a number of synthetic problems. I. Introduction This paper proposes an online learning algorithm for training a logistic regression model on nonstationary classification problems. By nonstationary 1 we mean that the statistics of each class may vary with time or, equivalently from the classification perspective, that the optimal decision boundary changes with time. The simplest online algorithm for training a logistic regression m...
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... In the following, the models exploited to define the two criteria used to decide when to query the labels are introduced. The two criteria are label uncertainty defined through logistic regression [25] and density-based criterion defined through Growing Gaussian Mixture Model (GGMM) [1]. ...
... In order to calculate the expression p(θ t |θ t−1 ), we must specify how the parameters change over time. Following [25], we assume no knowledge of the drifting distribution p(θ t |θ t−1 ). Thus, Eq. (15) can be eliminated by estimating p(y t |x t , D t−1 ) which is done as follows: ...
... 2) Handling of concept drift: In-non stationary setting, a variant version of (21) proposed in [25] is used. The situation is exactly the same as for the stationary case, except that the prior distribution is now N (µ t−1 , Σ t−1 + v t f ). ...
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... On the one hand, this approach is highly interpretable and supports relatively straightforward analyses of the impacts of different behavioural variables on state transition times; on the other hand, this may come at a cost to predictive accuracy around state boundaries. We furthermore 904 expect, given the challenge of overfitting with these datasets that motivated our sequential state constraint, that any comparable dynamic models with a continuous state space (eg (Penny & Roberts, 1999)) would be very difficult to suitably regularise. ...
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... MLR can be used to predict a response variable on the basis of continuous and/or categorical explanatory variables to determine the percent of variance in the response variable explained by the explanatory variables; to rank the relative importance of independents to assess interaction effects; and to understand the impact of covariate control variables. MLR allows the simultaneous comparison of more than one contrast ,that is the log odds of three or more contrasts are estimated simultaneously (Garson, 2009). If the response variable has more than two values, and there is no natural ordering of the categories, it called Multinomial Logistic Regression. ...
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