Learning general sparse additive models ...
Document type :
Article dans une revue scientifique: Article original
Title :
Learning general sparse additive models from point queries in high dimensions
Author(s) :
Tyagi, Hemant [Auteur]
MOdel for Data Analysis and Learning [MODAL]
Vybiral, Jan [Auteur]
Czech Technical University in Prague [CTU]
MOdel for Data Analysis and Learning [MODAL]
Vybiral, Jan [Auteur]
Czech Technical University in Prague [CTU]
Journal title :
Constructive Approximation
Pages :
403–455
Publisher :
Springer Verlag
Publication date :
2019-05-03
ISSN :
0176-4276
English keyword(s) :
Sparse additive models
sampling
hash functions
sparse recovery Mathematics
sampling
hash functions
sparse recovery Mathematics
HAL domain(s) :
Mathématiques [math]
English abstract : [en]
We consider the problem of learning a $d$-variate function $f$ defined on the cube $[−1, 1]^d ⊂ R^d$ , where the algorithm is assumed to have black box access to samples of f within this domain. Denote $S_r ⊂ {[d] \choose ...
Show more >We consider the problem of learning a $d$-variate function $f$ defined on the cube $[−1, 1]^d ⊂ R^d$ , where the algorithm is assumed to have black box access to samples of f within this domain. Denote $S_r ⊂ {[d] \choose r} ; r = 1,. .. , r_0$ to be sets consisting of unknown $r$-wise interactions amongst the coordinate variables. We then focus on the setting where f has an additive structure, i.e., it can be represented as $f = \sum_{j∈S1} φ_j + \sum_{j∈S2} φ_j + · · · + \sum_{j∈S_{r_0}} φ_j$, where each $φ_j ; j ∈ S_r$ is at most r-variate for $1 ≤ r ≤ r_0$. We derive randomized algorithms that query f at carefully constructed set of points, and exactly recover each $S_r$ with high probability. In contrary to the previous work, our analysis does not rely on numerical approximation of derivatives by finite order differences.Show less >
Show more >We consider the problem of learning a $d$-variate function $f$ defined on the cube $[−1, 1]^d ⊂ R^d$ , where the algorithm is assumed to have black box access to samples of f within this domain. Denote $S_r ⊂ {[d] \choose r} ; r = 1,. .. , r_0$ to be sets consisting of unknown $r$-wise interactions amongst the coordinate variables. We then focus on the setting where f has an additive structure, i.e., it can be represented as $f = \sum_{j∈S1} φ_j + \sum_{j∈S2} φ_j + · · · + \sum_{j∈S_{r_0}} φ_j$, where each $φ_j ; j ∈ S_r$ is at most r-variate for $1 ≤ r ≤ r_0$. We derive randomized algorithms that query f at carefully constructed set of points, and exactly recover each $S_r$ with high probability. In contrary to the previous work, our analysis does not rely on numerical approximation of derivatives by finite order differences.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
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