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The Rabin tree theorem yields an algorithm to solve the satisfiability problem for monadic second-order logic over infinite trees. Here we solve the probabilistic variant of this problem. Namely, we show how to compute the probability that…
Extreme multi-label classification (XMLC) is a learning task of tagging instances with a small subset of relevant labels chosen from an extremely large pool of possible labels. Problems of this scale can be efficiently handled by organizing…
We find upper bounds for the probability of underestimation and overestimation errors in penalized likelihood context tree estimation. The bounds are explicit and applies to processes of not necessarily finite memory. We allow for general…
We study the problem of computing the tightest upper and lower bounds on the probability that the sum of $n$ dependent Bernoulli random variables exceeds an integer $k$. Under knowledge of all pairs of bivariate distributions denoted by a…
An {\em ancestry labeling scheme} labels the nodes of any tree in such a way that ancestry queries between any two nodes in a tree can be answered just by looking at their corresponding labels. The common measure to evaluate the quality of…
We study online active learning for classifying streaming instances within the framework of statistical learning theory. At each time, the learner either queries the label of the current instance or predicts the label based on past seen…
We introduce algorithms for online, full-information prediction that are competitive with contextual tree experts of unknown complexity, in both probabilistic and adversarial settings. We show that by incorporating a probabilistic framework…
In the graph label selection problem, one is given an $n$-vertex graph and a budget $k$, and seeks to select $k$ vertices whose labels enable accurate prediction of the labels on the remaining vertices. This problem formalizes distilling a…
Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees,…
We consider the NP-hard Tree Containment problem that has important applications in phylogenetics. The problem asks if a given leaf-labeled network contains a subdivision of a given leaf-labeled tree. We develop a fast algorithm for the…
This paper tightens the best known analysis of Hein's 1989 algorithm to infer the topology of a weighted tree based on the lengths of paths between its leaves. It shows that the number of length queries required for a degree-$k$ tree of $n$…
Active regression considers a linear regression problem where the learner receives a large number of data points but can only observe a small number of labels. Since online algorithms can deal with incremental training data and take…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
Many machine learning tasks admit multiple models that perform almost equally well, a phenomenon known as predictive multiplicity. A fundamental source of this multiplicity is observational multiplicity, which arises from the stochastic…
Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…
Online machine learning systems need to adapt to domain shifts. Meanwhile, acquiring label at every timestep is expensive. We propose a surprisingly simple algorithm that adaptively balances its regret and its number of label queries in…
Labeling schemes seek to assign a short label to each node in a network, so that a function on two nodes can be computed by examining their labels alone. For the particular case of trees, optimal bounds (up to low order terms) were recently…
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.…
Here we study the problem of learning labels for large text corpora where each text can be assigned a variable number of labels. The problem might seem trivial when the label dimensionality is small and can be easily solved using a series…
Recent research revealed the existence of gaps in the complexity landscape of locally checkable labeling (LCL) problems in the LOCAL model of distributed computing. For example, the deterministic round complexity of any LCL problem on…