A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Probabilistic models learned as density estimators can be exploited in representation learning beside being toolboxes used to answer inference queries only. However, how to extract useful representations highly depends on the particular model involved. We argue that tractable inference, i.e. inference that can be compu…
A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally tractable. Here, we develop an approach that simultaneously achieves both flexibility and…
In this paper we present decomposable priors, a family of priors over structure and parameters of tree belief nets for which Bayesian learning with complete observations is tractable, in the sense that the posterior is also decomposable and can be completely determined analytically in polynomial time. This follows from…
Casting neural networks in generative frameworks is a highly sought-after endeavor these days. Contemporary methods, such as Generative Adversarial Networks, capture some of the generative capabilities, but not all. In particular, they lack the ability of tractable marginalization, and thus are not suitable for many ta…
We study the computational tractability of PAC reinforcement learning with rich observations. We present new provably sample-efficient algorithms for environments with deterministic hidden state dynamics and stochastic rich observations. These methods operate in an oracle model of computation -- accessing policy and va…
We consider the problem of transforming samples from one continuous source distribution into samples from another target distribution. We demonstrate with optimal transport theory that when the source distribution can be easily sampled from and the target distribution is log-concave, this can be tractably solved with c…
Despite the fundamental nature of the inhomogeneous Poisson process in the theory and application of stochastic processes, and its attractive generalizations (e.g. Cox process), few tractable nonparametric modeling approaches of intensity functions exist, especially when observed points lie in a high-dimensional space.…
We introduce RNADE, a new model for joint density estimation of real-valued vectors. Our model calculates the density of a datapoint as the product of one-dimensional conditionals modeled using mixture density networks with shared parameters. RNADE learns a distributed representation of the data, while having a tractab…
Information theoretic active learning has been widely studied for probabilistic models. For simple regression an optimal myopic policy is easily tractable. However, for other tasks and with more complex models, such as classification with nonparametric models, the optimal solution is harder to compute. Current approach…
We present a novel tractable generative model that extends Sum-Product Networks (SPNs) and significantly boosts their power. We call it Sum-Product-Quotient Networks (SPQNs), whose core concept is to incorporate conditional distributions into the model by direct computation using quotient nodes, e.g. $P(A|B) = \frac{P(…
Many polynomial invariants of knots and links, including the Jones and HOMFLY-PT polynomials, are widely used in practice but #P-hard to compute. It was shown by Makowsky in 2001 that computing the Jones polynomial is fixed-parameter tractable in the treewidth of the link diagram, but the parameterised complexity of th…
Despite widespread interest and practical use, the theoretical properties of random forests are still not well understood. In this paper we contribute to this understanding in two ways. We present a new theoretically tractable variant of random regression forests and prove that our algorithm is consistent. We also prov…