Related papers: Context Tree Selection: A Unifying View
We consider the problem of how to improve automatic target recognition by fusing the naive sensor-level classification decisions with "intuition," or context, in a mathematically principled way. This is a general approach that is compatible…
Pairwise Choice Markov Chains (PCMC) have been recently introduced to overcome limitations of choice models based on traditional axioms unable to express empirical observations from modern behavior economics like context effects occurring…
This paper is a variation on the uniform spanning tree theme. We use random spanning forests to solve the following problem: for a Markov process on a finite set of size $n$, find a probability law on the subsets of any given size $m \leq…
This work introduces a notion of approximate probabilistic trace equivalence for labelled Markov chains, and relates this new concept to the known notion of approximate probabilistic bisimulation. In particular this work shows that the…
Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…
In this work we present a hierarchy of generalized contextuality. It refines the traditional binary distinction between contextual and noncontextual theories, and facilitates their comparison based on how contextual they are. Our approach…
We consider the problem of estimating the context tree of a stationary ergodic process with finite alphabet without imposing additional conditions on the process. As a starting point we introduce a Hamming metric in the space of irreducible…
Machine learning algorithms such as linear regression, SVM and neural network have played an increasingly important role in the process of scientific discovery. However, none of them is both interpretable and accurate on nonlinear datasets.…
The Stochastic Context Tree (SCOT) is a useful tool for studying infinite random sequences generated by an m-Markov Chain (m-MC). It captures the phenomenon that the probability distribution of the next state sometimes depends on less than…
Many efficient algorithms with strong theoretical guarantees have been proposed for the contextual multi-armed bandit problem. However, applying these algorithms in practice can be difficult because they require domain expertise to build…
Dealing with datasets of very high dimension is a major challenge in machine learning. In this paper, we consider the problem of feature selection in applications where the memory is not large enough to contain all features. In this…
The problems of model and variable selections for classification trees are jointly considered. A penalized criterion is proposed which explicitly takes into account the number of variables, and a risk bound inequality is provided for the…
We introduce context augmentation, a data-augmentation approach that uses large language models (LLMs) to generate contexts around observed strings as a means of facilitating valid frequentist inference. These generated contexts serve to…
The context tree source is a source model in which the occurrence probability of symbols is determined from a finite past sequence, and is a broader class of sources that includes i.i.d. and Markov sources. The proposed source model in this…
We propose ContextLM, a framework that implicitly learns multi-token prediction by augmenting standard pretraining with an intrinsic next-context prediction objective. ContextLM builds a language model on top of context embeddings that span…
Markov networks are popular models for discrete multivariate systems where the dependence structure of the variables is specified by an undirected graph. To allow for more expressive dependence structures, several generalizations of Markov…
Multinomial processing tree (MPT) models are tools for disentangling the contributions of latent cognitive processes in a given experimental paradigm. The present note analyzes MPT models subject to order constraints on subsets of its…
Traditional studies of memory for meaningful narratives focus on specific stories and their semantic structures but do not address common quantitative features of recall across different narratives. We introduce a statistical ensemble of…
Deep learning has shown state-of-art classification performance on datasets such as ImageNet, which contain a single object in each image. However, multi-object classification is far more challenging. We present a unified framework which…
With a large proportion of people carrying location-aware smartphones, we have an unprecedented platform from which to understand individuals and predict their future actions. This work builds upon the Context Tree data structure that…