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…
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48 results for “Tractable Algorithms”
We call an Ising model tractable when it is possible to compute its partition function value (statistical inference) in polynomial time. The tractability also implies an ability to sample configurations of this model in polynomial time. The notion of tractability extends the basic case of planar zero-field Ising models…
New bandit algorithm works without realizability assumption.
problem Contextual bandit problems without realizability assumption.
method Computes a constrained regression problem in every epoch, ensuring similar regret guarantees as realizability-based algorithms.
result Ensures similar regret guarantees as realizability-based algorithms, up to a misspecification term.
Fixed-parameter tractable computation of Reshetikhin--Turaev knot polynomials via tensor networksmath.GT
New algorithm speeds up knot polynomial calculations.
problem Computing Reshetikhin--Turaev knot polynomials efficiently.
method Fixed-parameter tractable computation via tensor networks.
result Knot polynomial computations are fixed-parameter tractable.
In this article we propose a Weighted Stochastic Mesh (WSM) Algorithm for approximating the value of a discrete and continuous time optimal stopping problem. We prove that in the discrete case the WSM algorithm leads to semi-tractability of the corresponding optimal problems in the sense that its complexity is bounded …
New algorithm achieves optimal regret in average reward MDPs without prior bias information.
problem Achieving optimal regret in average reward MDPs with computational efficiency and without prior bias information.
method Projective Mitigated Extended Value Iteration (PMEVI) to compute bias-constrained optimal policies efficiently.
result First tractable algorithm with minimax optimal regret of .
Develops a computationally tractable high-dimensional differential privacy estimator.
problem Differential privacy in high dimensions is computationally intractable.
method Combines high-dimensional robust statistics with differential privacy techniques.
result A computationally tractable algorithm with dimension-independent privacy loss.
Paper introduces md-vtrees for efficient probabilistic and causal inference.
problem Efficient inference in complex probabilistic models.
method Introduces md-vtrees to generalize tractability conditions for advanced inference queries.
result Derives first polytime algorithms for causal inference queries.
To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an exponential-time enumeration. However, asymptotically most graphs do not result in …
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…
Fixed-parameter tractability of private synthetic data generation
problem Generating synthetic data under differential privacy
method Linear programming and subsampled private multiplicative weights method
result Optimal error rates across all regimes
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…
In intractable, undirected graphical models, an intuitive way of creating structured mean field approximations is to select an acyclic tractable subgraph. We show that the hardness of computing the objective function and gradient of the mean field objective qualitatively depends on a simple graph property. If the tract…
On Computationally Tractable Selection of Experiments in Measurement-Constrained Regression Modelsstat.ML
We derive computationally tractable methods to select a small subset of experiment settings from a large pool of given design points. The primary focus is on linear regression models, while the technique extends to generalized linear models and Delta's method (estimating functions of linear regression models) as well. …
Computing expected predictions of discriminative models is a fundamental task in machine learning that appears in many interesting applications such as fairness, handling missing values, and data analysis. Unfortunately, computing expectations of a discriminative model with respect to a probability distribution defined…
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…
New characterization limits sampling with inexact scores.
problem Limiting sampling with inexact scores for unbiased results.
method Characterized types of inexact score oracle access.
result Weaker error assumptions rule out tractability of unbiased sampling.
New algorithm for context bandits with continuous actions.
problem Efficient decision-making with unknown action structures.
method Reduction-style algorithm combining supervised learning.
result Proven to work in general and validated with experiments.
New model generates data on constrained sets without losing tractability.
problem Generating data on constrained sets without losing tractability.
method Mirror Diffusion Models (MDM) learn diffusion processes in a dual space constructed from a mirror map.
result MDM generates data on convex constrained sets without losing tractability.
Ensemble Samplingstat.ML
Thompson sampling has emerged as an effective heuristic for a broad range of online decision problems. In its basic form, the algorithm requires computing and sampling from a posterior distribution over models, which is tractable only for simple special cases. This paper develops ensemble sampling, which aims to approx…
Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a mixture of densities by greedily adding components to the mixture. However, as i…
Unified framework for tractable inference scenarios in machine learning models.
problem Complex inference scenarios in machine learning models.
method Characterization of tractable modular operations over circuits and derivation of a unified framework.
result Unified framework for reasoning about tractable models.
The mean field methods, which entail approximating intractable probability distributions variationally with distributions from a tractable family, enjoy high efficiency, guaranteed convergence, and provide lower bounds on the true likelihood. But due to requirement for model-specific derivation of the optimization equa…
The Schatten-p quasi-norm is usually used to replace the standard nuclear norm in order to approximate the rank function more accurately. However, existing Schatten-p quasi-norm minimization algorithms involve singular value decomposition (SVD) or eigenvalue decomposition (EVD) in each iteration, and thus may…
The Schatten quasi-norm was introduced to bridge the gap between the trace norm and rank function. However, existing algorithms are too slow or even impractical for large-scale problems. Motivated by the equivalence relation between the trace norm and its bilinear spectral penalty, we define two tractable Schatten norm…
Large SVARsecon.EM
New algorithm speeds up SVAR inference for large datasets.
problem Inference in sign-identified SVARs for big data.
method Elliptical slice within Gibbs sampler for computational efficiency.
result Algorithm delivers posterior distribution and is well-defined.
New algorithm tackles non-linear utility in MNL bandits with regret.
problem Sequential assortment selection with intricate user-item interactions.
method Upper Confidence Bound principle for non-linear parametric utility functions, including neural networks.
result Achieves regret bound for neural network-based utilities.
Simplifies inference for simulators with or without tractable likelihoods.
problem Inference for models with intractable likelihoods.
method Amortized simulation-based frequentist inference.
result Valid confidence sets for parameter inference.
PNCs balance tractability and expressiveness in probabilistic modeling.
problem Balancing tractability and expressiveness in probabilistic models.
method Introduce probabilistic neural circuits (PNCs) as a mix of Bayesian networks and neural networks.
result PNCs are powerful function approximators.
The paper develops sum-of-squares relaxations for computing -divergences.
problem Computing -divergences from non-centered covariance matrices.
method Sum-of-squares relaxations for convex optimization.
result Sum-of-squares relaxations make computations tractable.
The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising models with homogeneous pairwise potentials but arbitrary (inhomogeneous) unary pot…
New lower bounds improve logistic log-likelihood optimization and inference.
problem Designing computationally tractable lower bounds for logistic log-likelihoods.
method Developed a piece-wise quadratic lower bound that uniformly improves tangent quadratic minorizers.
result Improves the speed of convergence and accuracy of variational Bayes approximations.
Bayesian network classifiers are used in many fields, and one common class of classifiers are naive Bayes classifiers. In this paper, we introduce an approach for reasoning about Bayesian network classifiers in which we explicitly convert them into Ordered Decision Diagrams (ODDs), which are then used to reason about t…
New algorithms compute robustness bounds for multiclass classification models.
problem Computing robustness of deep learning models in multiclass classification.
method Optimal transport and linear programming/entropic regularization.
result Tractable algorithms for computing robustness bounds.
Unified tractability conditions for various compositional inference queries.
problem Analyzing tractability of probabilistic and causal inference queries.
method Algebraic perspective on circuits, focusing on semiring operators.
result Unified sufficient conditions for tractable composition of operators.
XSPNs combine SPNs and MEVMs for efficient inference in data with repeated parts.
problem Efficient inference in data with repeated interchangeable parts.
method Introducing Exchangeability-Aware Sum-Product Networks (XSPNs) that combine SPNs and MEVMs.
result XSPNs can be more accurate than conventional SPNs when data contains repeated parts.
We study the fundamental tradeoffs between statistical accuracy and computational tractability in the analysis of high dimensional heterogeneous data. As examples, we study sparse Gaussian mixture model, mixture of sparse linear regressions, and sparse phase retrieval model. For these models, we exploit an oracle-based…
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…
Efficiently learns private models using public data.
problem Improving private learning performance with public data.
method Proves computationally efficient algorithms for private learning with public data.
result First computationally efficient algorithms for private learning with public data.
This paper advances sample-efficient learning for partially observable RL by introducing B-stability and new algorithms.
problem Hard sample complexity for learning near-optimal policies in partially observable RL.
method Proposes B-stability as a unified structural condition and develops new algorithms for sample-efficient learning.
result Any B-stable PSR can be learned with polynomial samples, improving over current best complexities.
New algorithms improve robust estimation in contaminated Gaussian models.
problem Simultaneous estimation of location and variance matrix in contaminated Gaussian models.
method Tractable adversarial algorithms with spline discriminators for robust estimation.
result Achieve minimax optimal rates or near-optimal rates under Huber's contamination model.
New algorithm tackles multimodal bandits with optimal regret bounds.
problem Stochastic multi-armed bandit problem with multimodal rewards.
method Proposed computationally tractable algorithm for multimodal rewards.
result Asymptotically optimal algorithms implemented for the bandit problem.
In graph theory, Courcelle's theorem essentially states that, if an algorithmic problem can be formulated in monadic second-order logic, then it can be solved in linear time for graphs of bounded treewidth. We prove such a metatheorem for a general class of triangulations of arbitrary fixed dimension d, including all t…
The stochastic block model (SBM) is a generative model revealing macroscopic structures in graphs. Bayesian methods are used for (i) cluster assignment inference and (ii) model selection for the number of clusters. In this paper, we study the behavior of Bayesian inference in the SBM in the large sample limit. Combinin…
We compute the categorified sl(N) link invariants as defined by Khovanov and Rozansky, for various links and values of N. This is made tractable by an algorithm for reducing tensor products of matrix factorisations to finite rank, which we implement in the computer algebra package Singular.
Paper tackles reinforcement learning with complex observations and simple latent dynamics.
problem Understanding reinforcement learning with complex observations and simple latent dynamics.
method Statistical and algorithmic analysis of reinforcement learning under general latent dynamics.
result Identifies latent pushforward coverability as a condition for statistical tractability.
Optimizes ICA performance in high dimensions with computational constraints.
problem Statistical optimality and computational tractability in ICA.
method Characterization of optimal sample complexity, development of computationally tractable estimates.
result Optimal sample complexity is linear in dimensionality, quadratic with low-degree polynomial algorithms.
We consider the problem of Bayesian learning on sensitive datasets and present two simple but somewhat surprising results that connect Bayesian learning to "differential privacy:, a cryptographic approach to protect individual-level privacy while permiting database-level utility. Specifically, we show that that under s…