Universal Codes from Switching Strategies

We discuss algorithms for combining sequential prediction strategies, a task which can be viewed as a natural generalisation of the concept of universal coding. We describe a graphical language based on Hidden Markov Models for defining prediction strategies, and we provide both existing and new models as examples. The models include efficient, parameterless models for switching between the input strategies over time, including a model for the case where switches tend to occur in clusters, and finally a new model for the scenario where the prediction strategies have a known relationship, and where jumps are typically between strongly related ones. This last model is relevant for coding time series data where parameter drift is expected. As theoretical ontributions we introduce an interpolation construction that is useful in the development and analysis of new algorithms, and we establish a new sophisticated lemma for analysing the individual sequence regret of parameterised models

A closer look at adaptive regret

For the prediction with expert advice setting, we consider methods to construct algorithms that have low adaptive regret. The adaptive regret of an algorithm on a time interval [t1,t2] is the loss of the algorithm minus the loss of the best expert over that interval. Adaptive regret measures how well the algorithm approximates the best expert locally, and so is different from, although closely related to, both the classical regret, measured over an initial time interval [1,t], and the tracking regret, where the algorithm is compared to a good sequence of experts over [1,t]. We investigate two existing intuitive methods for deriving algorithms with low adaptive regret, one based on specialist experts and the other based on restarts. Quite surprisingly, we show that both methods lead to the same algorithm, namely Fixed Share, which is known for its tracking regret. We provide a thorough analysis of the adaptive regret of Fixed Share. We obtain the exact worst-case adaptive regret for Fixed Share, from which the classical tracking bounds follow. We prove that Fixed Share is

A closer look at adaptive regret

For the prediction with expert advice setting, we consider methods to construct algorithms that have low adaptive regret. The adaptive regret of an algorithm on a time interval [t1,t2] is the loss of the algorithm minus the loss of the best expert over that interval. Adaptive regret measures how well the algorithm approximates the best expert locally, and so is different from, although closely related to, both the classical regret, measured over an initial time interval [1,t], and the tracking regret, where the algorithm is compared to a good sequence of experts over [1,t]. We investigate two existing intuitive methods for deriving algorithms with low adaptive regret, one based on specialist experts and the other based on restarts. Quite surprisingly, we show that both methods lead to the same algorithm, namely Fixed Share, which is known for its tracking regret. We provide a thorough analysis of the adaptive regret of Fixed Share. We obtain the exact worst-case adaptive regret for Fixed Share, from which the classical tracking bounds follow. We prove that Fixed Share is optimal for adaptive regret: the worst-case adaptive regret of any algorithm is at least that of an instance of Fixed Share

Active citizenship: participatory patterns of European youth

Purpose: Treating Active Citizenship as a sum of behavioural indicators requires certain prerequisites that can be difficult to meet in practice (e.g. structural validity and measurement invariance). We explore a different approach, in which we treat Active Citizenship as a categorical, rather than a linear, construct. Design: Based on longitudinal data from eight European countries, we discovered the patterns’ structure based on the first-year data and then replicated the analysis on the second-year sample to confirm it. Next, we explored the change between the years and its’ trajectories. We compared countries profiles and their change. Finally, we used multinomial logistic regression to explore the most common trajectories. Findings: We describe six patterns: fighter, activist, volunteer, backer, online and indifferent. The pattern structure is replicable and 41.8% of respondents preserve their pattern. For those respondents who changed their pattern, we identified political interest, religiosity, gender and age as the main factors behind this change. Research implications: The study contributes to the understanding of youth Active Citizenship and the factors that support and promote it

Efficient tracking of a growing number of experts

International audienceWe consider a variation on the problem of prediction with expert advice, where new forecasters that were unknown until then may appear at each round. As often in prediction with expert advice, designing an algorithm that achieves near-optimal regret guarantees is straightforward, using ag-gregation of experts. However, when the comparison class is sufficiently rich, for instance when the best expert and the set of experts itself changes over time, such strategies naively require to maintain a prohibitive number of weights (typically exponential with the time horizon). By contrast, designing strategies that both achieve a near-optimal regret and maintain a reasonable number of weights is highly non-trivial. We consider three increasingly challenging objectives (simple regret, shifting regret and sparse shifting regret) that extend existing notions defined for a fixed expert ensemble; in each case, we design strategies that achieve tight regret bounds, adaptive to the parameters of the comparison class, while being computationally inexpensive. Moreover, our algorithms are anytime , agnostic to the number of incoming experts and completely parameter-free. Such remarkable results are made possible thanks to two simple but highly effective recipes: first the " abstention trick " that comes from the specialist framework and enables to handle the least challenging notions of regret, but is limited when addressing more sophisticated objectives. Second, the " muting trick " that we introduce to give more flexibility. We show how to combine these two tricks in order to handle the most challenging class of comparison strategies