Distribution to Distribution Regression

By Junier B. Oliva, Barnab'as P'oczos, Jeff Schneider. 2013

90 citations recorded by the source corpus.

Subfields: Probabilistic & Bayesian Methods

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In Probabilistic & Bayesian Methods

Citations in the corpus

Deep Perm-Set Net: Learn to predict sets with unknown permutation and cardinality using deep neural networks (2018, background): “…as mixture models Blei et al. (2003); Hannah et al. (2011); Tran et al. (2016), learning distributions from a set of samples Muandet et al. (2012); Oliva et al. (2013), model-based multiple instance learning Vo et al. (2017) and novelty detection from point pattern data Vo et al. (2016), can be…”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “Secondly, compared to density estimation approaches (Póczos et al. 2011, Oliva et al. 2014; 2013), the kernel mean representation is less prone to the curse of dimensionality and admits fast convergence in terms of sample size (Shawe-Taylor and Cristianini 2004, Smola et al. 2007, Grünewälder et…”
Set Transformer (2018, background): “…shape recognition (Wu et al., 2015; Shi et al., 2015; Su et al., 2015; Charles et al., 2017), sequence ordering (Vinyals et al., 2016), and various set operations (Muandet et al., 2012; Oliva et al., 2013; Edwards & Storkey, 2017; Zaheer et al., 2017) can also be viewed as the set-input problems.”
Prototypal Analysis and Prototypal Regression (2017, methodology): “Oliva et al. (2013) introduces a distribution to distribution regression model via orthogonal series density estimation on the response distributions and kernel density estimation on the predictor distributions and the new input.”
Fast Distribution To Real Regression (2013, background): “ through observations of (X;Y) pairs that are often taken to be an arbitrarily dense grid in the domain of the functions. For a comprehensive survey in functional analysis see [1, 18]. Also, recently [13] studied the problem of distribution to distribution regression, where both input and output cov”
Deep Sets (2017, methodology): “Supervised learning examples include tasks like estimation of population statistics (Poczos et al., 2013), where applications range from giga-scale cosmology (Ntampaka et al., 2016; Ravanbakhsh et al., 2016a) to nano-scale quantum chemistry (Faber et al., 2016).”
Asymptotically Exact, Embarrassingly Parallel MCMC (2013, unknown): “Following work in density-based regression [15], we use an estimate of the L2 distance, d2(p, p̂), between the groundtruth posterior density p and a proposed posterior density p̂, where d2(p, p̂) = ‖p− p̂‖2 = (∫ (p(θ)− p̂(θ))(2)dθ )1/2 .”
Operator-valued Kernels for Learning from Functional Response Data (2015, background): “There are also other papers that deal with machine learning problems where covariates are probability distributions and discuss their relation with FDA (Poczos et al., 2012, 2013; Oliva et al., 2013).”
Two-stage sampled learning theory on distributions (2014, background): “[20] Junier Oliva, Barnabás Póczos, and Jeff Schneider.”
Learn to Predict Sets Using Feed-Forward Neural Networks (2020, background): “Approaches such as mixture models [31], [39], [40], learning distributions from a set of samples [41], [42], model-based multiple instance learning [43], and novelty detection from point pattern data [44], can be counted as few out many examples that use point patterns or sets as input or output and”
Fast Function to Function Regression (2014, unknown): “That is, if we consider F as a functional Hilbert space, where f ∈ F is such that f : Gx 7→ Gy , then f is estimated by f∗ = arg minf̂ ∑N i=1‖qi − f̂(pi)‖2Gy + λ‖f‖ 2 F .”
Joint Learning of Set Cardinality and State Distribution (2017, background): “…(Blei, Ng, and Jordan 2003; Hannah, Blei, and Powell 2011; Tran et al. 2016), learning distributions from a set of samples (Muandet et al. 2012; Oliva, Póczos, and Schneider 2013), model-based multiple instance learning (Vo et al. 2017) and novelty detection from point pattern data (Vo et al.…”
Neural networks for post-processing ensemble weather forecasts (2018, methodology): “Recently, ﬂexible distribution-to-distribution regression network models have been proposed in the machine learning literature (e.g., Oliva et al., 2013; Kou et al., 2018).”