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In this paper, we consider the revealed preferences problem from a learning perspective. Every day, a price vector and a budget is drawn from an unknown distribution, and a rational agent buys his most preferred bundle according to some…
We present a version of the fundamental theorem of asset pricing (FTAP) for continuous time large financial markets with two filtrations in an $L^p$-setting for $ 1 \leq p < \infty$. This extends the results of Yuri Kabanov and Christophe…
We investigate graph representation learning approaches that enable models to generalize across graphs: given a model trained using the representations from one graph, our goal is to apply inference using those same model parameters when…
Categorization axioms have been proposed to axiomatizing clustering results, which offers a hint of bridging the difference between human recognition system and machine learning through an intuitive observation: an object should be assigned…
Sorting is a common and ubiquitous activity for computers. It is not surprising that there exist a plethora of sorting algorithms. For all the sorting algorithms, it is an accepted performance limit that sorting algorithms are linearithmic…
Generalized sorting problem, also known as sorting with forbidden comparisons, was first introduced by Huang et al. together with a randomized algorithm which requires $\tilde O(n^{3/2})$ probes. We study this problem with additional…
We propose to study value automata with filters, a natural generalization of regular cost automata to nondeterminism. Models such as weighted automata and Parikh automata appear naturally as specializations. Results on the expressiveness of…
Progressive filtering is a simple way to perform hierarchical classification, inspired by the behavior that most humans put into practice while attempting to categorize an item according to an underlying taxonomy. Each node of the taxonomy…
Most recent CNN architectures use average pooling as a final feature encoding step. In the field of fine-grained recognition, however, recent global representations like bilinear pooling offer improved performance. In this paper, we…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
Natural Language Processing has moved rather quickly from modelling specific tasks to taking more general pre-trained models and fine-tuning them for specific tasks, to a point where we now have what appear to be inherently generalist…
We use Markov categories to generalize the basic theory of Markov chains and hidden Markov models to an abstract setting. This comprises characterizations of hidden Markov models in terms of conditional independences and algorithms for…
We investigate the data distribution valuation problem, which aims to quantify the values of data distributions from their samples. This is a recently proposed problem that is related to but different from classical data valuation and can…
Generalized planning is concerned with the computation of general policies that solve multiple instances of a planning domain all at once. It has been recently shown that these policies can be computed in two steps: first, a suitable…
Generative flow networks (GFlowNets) are amortized variational inference algorithms that are trained to sample from unnormalized target distributions over compositional objects. A key limitation of GFlowNets until this time has been that…
Lenses have a rich history and have recently received a great deal of attention from applied category theorists. We generalize the notion of lens by defining a category $\mathsf{Lens}_F$ for any category $\mathcal{C}$ and functor $F\colon…
Generalization in generative modeling is defined as the ability to learn an underlying distribution from a finite dataset and produce novel samples, with evaluation largely driven by held-out performance and perceived sample quality. In…
We introduce a category Prob of probability spaces whose objects are all probability spaces and arrows are corresponding to measurable functions satisfying an absolutely continuous requirement. We can consider a Prob-arrow as an evolving…
We introduce the Generalized Turing Test (GTT), a formal framework for comparing the capabilities of arbitrary agents via indistinguishability. For agents A and B, we define the Turing comparator A $\geq$ B to hold if B, acting as a…
We develop a fully Bayesian hierarchical model for trend filtering, itself a new development in nonparametric, univariate regression. The framework more broadly applies to the generalized lasso, but focus is on Bayesian trend filtering. We…