233,677 research outputs found
Sparse image reconstruction on the sphere: analysis and synthesis
We develop techniques to solve ill-posed inverse problems on the sphere by
sparse regularisation, exploiting sparsity in both axisymmetric and directional
scale-discretised wavelet space. Denoising, inpainting, and deconvolution
problems, and combinations thereof, are considered as examples. Inverse
problems are solved in both the analysis and synthesis settings, with a number
of different sampling schemes. The most effective approach is that with the
most restricted solution-space, which depends on the interplay between the
adopted sampling scheme, the selection of the analysis/synthesis problem, and
any weighting of the l1 norm appearing in the regularisation problem. More
efficient sampling schemes on the sphere improve reconstruction fidelity by
restricting the solution-space and also by improving sparsity in wavelet space.
We apply the technique to denoise Planck 353 GHz observations, improving the
ability to extract the structure of Galactic dust emission, which is important
for studying Galactic magnetism.Comment: 11 pages, 6 Figure
Sparse Image Reconstruction on the Sphere: Analysis and Synthesis
We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularization, exploiting sparsity in both axisymmetric and directional scale-discretized wavelet space. Denoising, in painting, and deconvolution problems and combinations thereof, are considered as examples. Inverse problems are solved in both the analysis and synthesis settings, with a number of different sampling schemes. The most effective approach is that with the most restricted solution-space, which depends on the interplay between the adopted sampling scheme, the selection of the analysis/synthesis problem, and any weighting of the ℓ1 norm appearing in the regularization problem. More efficient sampling schemes on the sphere improve reconstruction fidelity by restricting the solution-space and also by improving sparsity in wavelet space. We apply the technique to denoise Planck 353-GHz observations, improving the ability to extract the structure of Galactic dust emission, which is important for studying Galactic magnetism
Deterministic Sampling of Multivariate Densities based on Projected Cumulative Distributions
We want to approximate general multivariate probability density functions by
deterministic sample sets. For optimal sampling, the closeness to the given
continuous density has to be assessed. This is a difficult challenge in
multivariate settings. Simple solutions are restricted to the one-dimensional
case. In this paper, we propose to employ one-dimensional density projections.
These are the Radon transforms of the densities. For every projection, we
compute their cumulative distribution function. These Projected Cumulative
Distributions (PCDs) are compared for all possible projections (or a discrete
set thereof). This leads to a tractable distance measure in multivariate space.
The proposed approximation method is efficient as calculating the distance
measure mainly entails sorting in one dimension. It is also surprisingly simple
to implement.Comment: 21 pages, 10 figure
Context Attentive Bandits: Contextual Bandit with Restricted Context
We consider a novel formulation of the multi-armed bandit model, which we
call the contextual bandit with restricted context, where only a limited number
of features can be accessed by the learner at every iteration. This novel
formulation is motivated by different online problems arising in clinical
trials, recommender systems and attention modeling. Herein, we adapt the
standard multi-armed bandit algorithm known as Thompson Sampling to take
advantage of our restricted context setting, and propose two novel algorithms,
called the Thompson Sampling with Restricted Context(TSRC) and the Windows
Thompson Sampling with Restricted Context(WTSRC), for handling stationary and
nonstationary environments, respectively. Our empirical results demonstrate
advantages of the proposed approaches on several real-life datasetsComment: IJCAI 201
Approximately Sampling Elements with Fixed Rank in Graded Posets
Graded posets frequently arise throughout combinatorics, where it is natural
to try to count the number of elements of a fixed rank. These counting problems
are often -complete, so we consider approximation algorithms for
counting and uniform sampling. We show that for certain classes of posets,
biased Markov chains that walk along edges of their Hasse diagrams allow us to
approximately generate samples with any fixed rank in expected polynomial time.
Our arguments do not rely on the typical proofs of log-concavity, which are
used to construct a stationary distribution with a specific mode in order to
give a lower bound on the probability of outputting an element of the desired
rank. Instead, we infer this directly from bounds on the mixing time of the
chains through a method we call .
A noteworthy application of our method is sampling restricted classes of
integer partitions of . We give the first provably efficient Markov chain
algorithm to uniformly sample integer partitions of from general restricted
classes. Several observations allow us to improve the efficiency of this chain
to require space, and for unrestricted integer partitions,
expected time. Related applications include sampling permutations
with a fixed number of inversions and lozenge tilings on the triangular lattice
with a fixed average height.Comment: 23 pages, 12 figure
Memory Bounded Open-Loop Planning in Large POMDPs using Thompson Sampling
State-of-the-art approaches to partially observable planning like POMCP are
based on stochastic tree search. While these approaches are computationally
efficient, they may still construct search trees of considerable size, which
could limit the performance due to restricted memory resources. In this paper,
we propose Partially Observable Stacked Thompson Sampling (POSTS), a memory
bounded approach to open-loop planning in large POMDPs, which optimizes a fixed
size stack of Thompson Sampling bandits. We empirically evaluate POSTS in four
large benchmark problems and compare its performance with different tree-based
approaches. We show that POSTS achieves competitive performance compared to
tree-based open-loop planning and offers a performance-memory tradeoff, making
it suitable for partially observable planning with highly restricted
computational and memory resources.Comment: Presented at AAAI 201
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