In this paper, we develop and analyze techniques for recovering a linear image $Bx$ of an unknown signal $x$ from indirect noisy observation $\omega=Ax+\xi$. It is {\em a priori} known that $x\in \cX$, a given convex compact set, and that $x$ is $s$-sparse---has at most $s$ nonvanishing entries. The proposed estimates belong to a large family of recovery routines by $\ell_1$-minimization. However, unlike the classical result describing performance of such estimates, we do not make any special (and hard to check) assumptions about the sensing matrix $A$ such as nullspace or Restricted Isometry condition and the like. As a consequence, parameters of the estimates and the upper bounds on their risks are not available in a closed analytic form, but are delivered instead by efficient computation as solutions to explicit convex optimization problems.
We study sampling from a distribution supported on an unknown compact $d$-dimensional $C^2$ manifold $M\subset\mathbb{R}^D$, observed only through i.i.d. uniform points from $M$. We reconstruct the constraint using an adaptive local-convex-hull estimator and target an ambient distribution penalized by squared distance...
These certificate routines yield the first quadratic and subquadratic-time algorithms for robust sparse estimation for broad families of distributions and reduce a high-value sparse direction to a bounded-radius set in the graph of large correlations and searches the resulting candidate supports.
A high-probability uniform ($L^{\infty}$) recovery guarantee that jointly controls approximation and statistical errors while enjoying an optimization error of zero is introduced.
Rui-Yang Hong, Hrad Ghoukasian, Anastasis Kratsios· 0 citations
We study the estimation of a $K$-dimensional simplex from $N$ i.i.d.\ points sampled uniformly from its interior; the observations are convex combinations of $K+1$ unknown prototypes. Existing polynomial-time estimators need cubic per-sample work or $O(NK)$ storage and are impractical at $N\sim 10^6$--$10^8$. We propos...
The goal of this thesis is to consider two instances of a class of reconstruction problems that aim to recover an unknown signal x from indirect measurements m(x) that are algebraic in nature. Such problems are paramount in mathematics, enjoying applications in a wide array of fields like molecular imaging, machine lea...
The main innovation is to develop stochastic control theory within the branching OGP framework, significantly expanding the settings in which it locates an exact algorithmic threshold.
Brice Huang, Mark Sellke, Ni-Ke Sun· 3 citations· ⚡1
Adaptive AI agents can help make BIM data more machine-readable by navigating IFC models, interpreting inconsistent information, and mapping it to defined standards. In this blog, Alok Rawat shares findings from a real-world pilot in construction workflows. The post Adaptive AI Agents in Construction Workflows appeared first on GPT-Lab.
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