3 research outputs found
On similarity prediction and pairwise clustering
We consider the problem of clustering a finite set of items from pairwise similarity information. Unlike what is done in the literature on this subject, we do so in a passive learning setting, and with no specific constraints on the cluster shapes other than their size. We investigate the problem in different settings: i. an online setting, where we provide a tight characterization of the prediction complexity in the mistake bound model, and ii. a standard stochastic batch setting, where we give tight upper and lower bounds on the achievable generalization error. Prediction performance is measured both in terms of the ability to recover the similarity function encoding the hidden clustering and in terms of how well we classify each item within the set. The proposed algorithms are time efficient
On Similarity Prediction and Pairwise Clustering
International audienceWe consider the problem of clustering a finite set of items from pairwise similarity information. Unlike what is done in the literature on this subject, we do so in a passive learning setting, and with no specific constraints on the cluster shapes other than their size. We investigate the problem in different settings: i. an online setting, where we provide a tight characterization of the prediction complexity in the mistake bound model, and ii. a standard stochastic batch setting, where we give tight upper and lower bounds on the achievable generalization error. Prediction performance is measured both in terms of the ability to recover the similarity function encoding the hidden clustering and in terms of how well we classify each item within the set. The proposed algorithms are time efficient
Stochastic Contextual Bandits with Graph-based Contexts
We naturally generalize the on-line graph prediction problem to a version of
stochastic contextual bandit problems where contexts are vertices in a graph
and the structure of the graph provides information on the similarity of
contexts. More specifically, we are given a graph , whose vertex set
represents contexts with {\em unknown} vertex label . In our stochastic
contextual bandit setting, vertices with the same label share the same reward
distribution. The standard notion of instance difficulties in graph label
prediction is the cutsize defined to be the number of edges whose end
points having different labels. For line graphs and trees we present an
algorithm with regret bound of where is
the number of arms. Our algorithm relies on the optimal stochastic bandit
algorithm by Zimmert and Seldin~[AISTAT'19, JMLR'21]. When the best arm
outperforms the other arms, the regret improves to . The regret bound in the later case is comparable to other optimal
contextual bandit results in more general cases, but our algorithm is easy to
analyze, runs very efficiently, and does not require an i.i.d. assumption on
the input context sequence. The algorithm also works with general graphs using
a standard random spanning tree reduction