On Nonlinear Functions of Linear Combinations

By Persi Diaconis, Mehrdad Shahshahani. 1984

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Deep Learning in Finance (2016, background): “See Wold (1956), Diaconis and Shahshahani (1984), Ripley (1996), Cook (2007), and Hastie et al. (2009) for further discussion.”
Bond Risk Premia with Machine Learning∗ (2018, unknown): “The result is a powerful learning method which can approximate virtually any continuous function with compact support (see Kolmogorov, 1957; Diaconis and Shahshahani, 1984; Cybenko, 1989; Hornik, Stinchcombe and White, 1989).”
Deep learning for short-term traffic flow prediction (2016, background): “Diaconis and Shahshahani [1984] characterizes projection pursuit functions for a specific types of input functions.”
Modern Applied Statistics with S Fourth edition (2002, methodology): “Spence (2001) and Wilkinson (1999) and the classics of Tufte (1983, 1990, 1997) discuss the visual exploration of data.”
ON THE IDENTIFIABILITY OF ADDITIVE INDEX MODELS (2011, methodology): “In particular, it has been be shown that any square integrable function can be approximated to arbitrary precision by a function of form (1.1) (Diaconis and Shahshahani (1984)).”
Explainable Neural Networks based on Additive Index Models (2018, background): “In fact, as shown in Diaconis & Shahshahani (1984), the additive index models can approximate any multivariate function f ( x ) with arbitrary accuracy provided K , the number of ridge functions, is suﬃciently large.”
Learning Sparse Nonparametric DAGs (2019, background): “As long as M is sufficiently large, these functions are universal approximators (Diaconis and Shahshahani, 1984).”
Principles of Data Mining (2001, methodology): “Domingos (1999) provides a flexible methodology for converting any classification algorithm that operates on the assumption of 0–1 classification loss into a more general algorithm that can use any classification cost-matrix.”
Neural networks for pattern recognition (1995, background): “It is therefore not surprising that projection pursuit regression should have the same 'universal' approximation capabilities as multi-layer perceptrons (Diaconis and Shahshahani, 1984; Jones, 1987).”
Deep Portfolio Theory (2016, background): “prisingly, there are upper bounds on the number of terms, N2n+1 and Kn. With a careful choice of activation functions f i;f ij, this is enough to recover any multivariate portfolio payout function. Diaconis and Shahshahani (1984) demonstrated how basis functions can be constructed for a polynomial f”