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arXiv research

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.

168,657 papers · 148 categories

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1122 · Feb 201919922001200920172026
14 results for undercompleteness

This research develops an efficient reinforcement learning method for undercomplete POMDPs.

problem Learning undercomplete Partially Observable Markov Decision Processes (POMDPs) is computationally hard.
method OOM-UCB algorithm for episodic finite undercomplete POMDPs.
result Achieves optimal sample complexity of ildeO(1/ε2) ilde{\mathcal{O}}(1/\varepsilon^2) for finding an ε\varepsilon-optimal policy.

Single gradient step finds adversarial examples in random neural networks.

problem Finding adversarial examples in neural networks with random architectures.
method Gradient descent approach applied to random undercomplete and overcomplete two-layers neural networks.
result A single gradient step is sufficient to find adversarial examples in random neural networks.

New methods generalize nonlinear ICA beyond structural sparsity.

problem Identify true latent sources from nonlinear mixtures without structural sparsity assumptions.
method Propose identifiability results for undercomplete, partial sparsity, and flexible grouping structures.
result Prove identifiability in general settings of undercompleteness, partial sparsity, and flexible grouping structures.

We introduce the blind subspace deconvolution (BSSD) problem, which is the extension of both the blind source deconvolution (BSD) and the independent subspace analysis (ISA) tasks. We examine the case of the undercomplete BSSD (uBSSD). Applying temporal concatenation we reduce this problem to ISA. The associated `high …

2007-01-07abs ↗pdf ↗

PS4POMDPs algorithm simplifies online learning for episodic POMDPs with unknown models.

problem Learning in POMDPs is harder than in MDPs; online learning is especially challenging.
method Posterior Sampling-based reinforcement learning algorithm (PS4POMDPs)
result Bayesian regret scales as √number of episodes and is polynomial in other parameters.

We analyze the decomposition of a data matrix, assumed to be a superposition of a low-rank component and a component which is sparse in a known dictionary, using a convex demixing method. We provide a unified analysis, encompassing both undercomplete and overcomplete dictionary cases, and show that the constituent comp…

2019-02-21abs ↗pdf ↗

Traditional dictionary learning methods are based on quadratic convex loss function and thus are sensitive to outliers. In this paper, we propose a generic framework for robust dictionary learning based on concave losses. We provide results on composition of concave functions, notably regarding super-gradient computati…

2017-11-02abs ↗pdf ↗

The framework of variational autoencoders allows us to efficiently learn deep latent-variable models, such that the model's marginal distribution over observed variables fits the data. Often, we're interested in going a step further, and want to approximate the true joint distribution over observed and latent variables…

2019-07-10abs ↗pdf ↗

Two-layer neural networks need more neurons to be robust.

problem Understanding the robustness of two-layer neural networks and the role of overparametrization.
method Investigation of the tradeoffs between network size and robustness, using Lipschitz constant as a measure.
result A conjecture that robustness requires overparametrization, with precise bounds for different cases.

Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of interest, such as covariance, dynamical structure, correlation between data sets, inp…

2014-06-03abs ↗pdf ↗

Paper refutes conjecture on tensor power iteration convergence in overcomplete models.

problem Understanding convergence of tensor power iteration in overcomplete random tensors.
method Analysis of tensor power iteration dynamics from random initialization.
result Polynomially many steps are necessary for convergence, refutes logarithmic conjecture.