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Approximation theoretic advice for supervised learning

F75081afd76cac5bcea8bd43419e174e?s=47 Paul Constantine
September 29, 2018

Approximation theoretic advice for supervised learning

My presentation at the Approximation Theory and Machine Learning conference at Purdue, Sept 29, 2018

F75081afd76cac5bcea8bd43419e174e?s=128

Paul Constantine

September 29, 2018
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  1. Approximation theoretic advice for supervised learning PAUL CONSTANTINE Assistant Professor

    Department of Computer Science University of Colorado, Boulder activesubspaces.org! @DrPaulynomial! SLIDES AVAILABLE UPON REQUEST DISCLAIMER: These slides are meant to complement the oral presentation. Use out of context at your own risk.
  2. Even more understanding is lost if we consider each thing

    we can do to data only in terms of some set of very restrictive assumptions under which that thing is best possible—assumptions we know we CANNOT check in practice.
  3. data model noise parameter error uncertainty overfit TRIGGER WARNING!

  4. Selected regression / approximation / UQ literature My personal bibliography

    Ghanem and Spanos, Stochastic Finite Elements (Springer, 1991) Xiu and Karniadakis, The Wiener-Askey polynomial chaos (SISC, 2002) Nobile, Tempone, and Webster, A sparse grid stochastic collocation method (SINUM, 2008) Gautschi, Orthogonal Polynomials (Oxford UP, 2004) Koehler and Owen, Computer experiments (Handbook of Statistics, 1996) Jones, A taxonomy of global optimization methods based on response surfaces (JGO, 2001) Cook, Regression Graphics (Wiley, 1998)
  5. None
  6. Regression Approximation x y x y

  7. Regression x y { xi, yi } ⇡ ( x,

    y ) i.i.d. samples from unknown GIVEN GOAL statistically characterize y | x e.g., E[ y | x ] , Var[ y | x ]
  8. Regression { xi, yi } ⇡ ( x, y )

    i.i.d. samples from unknown GIVEN GOAL statistically characterize y | x e.g., E[ y | x ] , Var[ y | x ] y = p ( x, ✓ ) + " E[ y | x ] modeled r.v., zero-mean, independent of x x y MODEL (e.g., polynomials)
  9. Regression { xi, yi } ⇡ ( x, y )

    i.i.d. samples from unknown GIVEN GOAL statistically characterize y | x e.g., E[ y | x ] , Var[ y | x ] ˆ ✓ = argmin ✓ X i yi p ( xi, ✓ ) 2 y = p ( x, ✓ ) + " MODEL (e.g., polynomials) E[ y | x ] modeled r.v., zero-mean, independent of x x y FIT (e.g., max likelihood)
  10. Regression x y { xi, yi } ⇡ ( x,

    y ) i.i.d. samples from unknown GIVEN GOAL statistically characterize y | x e.g., E[ y | x ] , Var[ y | x ] ˆ ✓ = argmin ✓ X i yi p ( xi, ✓ ) 2 y = p ( x, ✓ ) + " E[ y | x ] modeled r.v., zero-mean, independent of x PREDICT E[ y | x ⇤ ] ⇡ p ( x ⇤ , ˆ ✓ ) = ˆ p ( x ⇤) MODEL (e.g., polynomials) FIT (e.g., max likelihood)
  11. Var[ y | x ⇤ ] ⇡ “formula” E[ y

    | x ⇤ ] ⇡ p ( x ⇤ , ˆ ✓ ) = ˆ p ( x ⇤) ˆ ✓ = argmin ✓ X i yi p ( xi, ✓ ) 2 y = p ( x, ✓ ) + " Regression x y { xi, yi } ⇡ ( x, y ) i.i.d. samples from unknown GIVEN GOAL statistically characterize y | x e.g., E[ y | x ] , Var[ y | x ] E[ y | x ] modeled r.v., zero-mean, independent of x FIT (e.g., max likelihood) PREDICT QUANTIFY UNCERTAINTY MODEL (e.g., polynomials)
  12. Regression Approximation x y x y

  13. k p⇤ f k = e⇤(n) Approximation continuous functions polynomials

    of degree n p⇤ = argmin p 2 Pn k p f k Does a unique, best approximation exist? polynomials How does the best error behave? continuous function Can we construct an approximation? Algorithm: Given f , compute ˆ p k ˆ p f k  C e⇤(n) And analyze its error?
  14. kˆ p fk Approximation a function GIVEN GOAL f (

    x ) ⇡ ( x ) find such that the error is small a known density ˆ p ( x ) x y
  15. kˆ p fk Approximation x y a function GIVEN GOAL

    f ( x ) ⇡ ( x ) find such that the error is small a known density CONSTRUCTION ˆ p ( x ) choose xi
  16. kˆ p fk Approximation x y a function GIVEN GOAL

    f ( x ) ⇡ ( x ) find such that the error is small a known density CONSTRUCTION ˆ p ( x ) choose xi compute yi = f ( xi)
  17. kˆ p fk Approximation x y GIVEN GOAL ⇡ (

    x ) find such that the error is small a known density CONSTRUCTION choose ˆ p ( x ) xi compute yi = f ( xi) fit ˆ p = argmin p 2 Pn X i yi p ( xi) 2 a function f ( x )
  18. Regression Approximation x y x y ˆ p = argmin

    p 2 Pn X i yi p ( xi) 2 ˆ ✓ = argmin ✓ X i yi p ( xi, ✓ ) 2
  19. Regression Approximation x y x y The story of the

    data and fitted curve is different. But does it matter? YES ˆ p = argmin p 2 Pn X i yi p ( xi) 2 ˆ ✓ = argmin ✓ X i yi p ( xi, ✓ ) 2
  20. REGRESSION VS. APPROXIMATION What is error?

  21. Regression Approximation x y x y Approximation error | ˆ

    p ( x ) f ( x ) | sup x | ˆ p ( x ) f ( x ) | Error norms Confidence interval ˆ p ( x ) ± 2 b se[ y | x ] plug-in estimate of standard error ✓Z | ˆ p ( x ) f ( x ) |2 ⇡ ( x ) dx ◆1/2
  22. REGRESSION VS. APPROXIMATION What is convergence?

  23. Regression Approximation x y x y

  24. Regression Approximation x y x y As data increases, root-n

    consistency ˆ ✓ ! ✓ ˆ p ( x ) ! p ( x ) “true” parameters
  25. Regression Approximation x y x y ˆ ✓ ! ✓

    ˆ p ( x ) ! p ( x ) “true” parameters As data increases, root-n consistency
  26. Regression Approximation x y x y ˆ ✓ ! ✓

    ˆ p ( x ) ! p ( x ) “true” parameters As data increases, root-n consistency ˆ p ( x ) f ( x ) ! 0 As the approximation class grows
  27. Regression Approximation x y x y ˆ ✓ ! ✓

    ˆ p ( x ) ! p ( x ) “true” parameters As data increases, root-n consistency ˆ p ( x ) f ( x ) ! 0 As the approximation class grows
  28. Regression Approximation x y x y ˆ ✓ ! ✓

    ˆ p ( x ) ! p ( x ) “true” parameters As data increases, root-n consistency ˆ p ( x ) f ( x ) ! 0 As the approximation class grows
  29. Regression Approximation x y x y ˆ ✓ ! ✓

    ˆ p ( x ) ! p ( x ) “true” parameters As data increases, root-n consistency ˆ p ( x ) f ( x ) ! 0 As the approximation class grows Convergence rate depends on •  high order derivatives •  size of region of analyticity •  Chebyshev coefficients •  … f ( x )
  30. None
  31. Gaussian process regression Radial basis approximation x y x y

  32. Gaussian process regression x y { xi, yi } pairs

    GIVEN
  33. Gaussian process regression x y { xi, yi } pairs

    GIVEN ASSUME one realization of a GP yi = g ( xi, ! ) <latexit 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  34. Gaussian process regression x y { xi, yi } pairs

    GIVEN ASSUME one realization of a GP among many possible realizations yi = g ( xi, ·) <latexit 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<latexit 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<latexit 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<latexit 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yi = g ( xi, ! ) <latexit 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<latexit 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<latexit 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<latexit 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  35. Gaussian process regression x y { xi, yi } pairs

    GIVEN ASSUME one realization of a GP among many possible realizations CORRELATION MODEL (e.g.) (x, x 0 ; ✓) = exp( | x x 0|2 /✓) <latexit 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<latexit 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yi = g ( xi, ·) <latexit 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yi = g ( xi, ! ) <latexit 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<latexit 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<latexit 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<latexit 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  36. (x, x 0 ; ✓) = exp( | x x

    0|2 /✓) <latexit 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<latexit 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<latexit 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<latexit 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Gaussian process regression x y { xi, yi } pairs GIVEN ASSUME one realization of a GP among many possible realizations CORRELATION MODEL (e.g.) yi = g ( xi, ·) <latexit 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<latexit 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yi = g ( xi, ! ) <latexit 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<latexit 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<latexit 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<latexit 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  37. (x, x 0 ; ✓) = exp( | x x

    0|2 /✓) <latexit 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<latexit 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<latexit 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<latexit 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Gaussian process regression x y { xi, yi } pairs GIVEN ASSUME one realization of a GP among many possible realizations CORRELATION MODEL (e.g.) yi = g ( xi, ·) <latexit 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<latexit 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yi = g ( xi, ! ) <latexit 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<latexit 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<latexit 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<latexit 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  38. (x, x 0 ; ✓) = exp( | x x

    0|2 /✓) <latexit 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<latexit 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<latexit 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<latexit 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Gaussian process regression { xi, yi } pairs GIVEN ASSUME one realization of a GP among many possible realizations CORRELATION MODEL (e.g.) FIT x y yi = g ( xi, ·) <latexit 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<latexit 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yi = g ( xi, ! ) <latexit 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<latexit 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<latexit 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<latexit 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maximize ✓ likelihood(✓; { xi, yi } ) <latexit 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<latexit 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  39. yi = g ( xi, ·) <latexit sha1_base64="OCKIFR8Z4i9tsF1/wXrUpjAecow=">AAAWLHicjZhNb9s2GMfV7q3z3tIVOe2izSjQAkFh57DtMqBNmqZJ3TRtYidOFBiUTEts9FaKcuwI/iy7bpd9ml2GYdd9jpGS7MjiP1kMBKH4/z18HpIi+VB27LNEtFp/3bn70ceffPrZvc8bX3z51dffrNz/tpdEKXdo14n8iB/bJKE+C2lXMOHT45hTEtg+PbLPN5V+NKY8YVF4KKYxPQuIG7IRc4iQVYOVB9MBM38x3UeTAVszLWcYiceDlWbrSSv/mXqhXRaaRvnbH9xfvWMNIycNaCgcnyTJabsVi7OMcMEcn84aVprQmDjnxKWnshiSgCZnWR79zHwoa4bmKOLyLxRmXlu1yEiQJNPAlmRAhJfUNVWJtNNUjH4+y1gYp4KGTuFolPqmiEw1FOaQceoIfyoLxOFMxmo6HuHEEXLAGg0r5tGYDakTBQEJh5klPcxO22eZZUf+UEUU+VmzPZs9bFichvRiAY6pU4AqJnuUQw2rRhAft9ZoPDQ3Cy6RRaWaaRxTbjpynvWo6JTOck/ZjvKiBf1MqjRMUk5VNAX5bAbRDYBuYHQToJsYfQ7Q5xjdAugWRl8A9AVGtwG6jdGXAH2J0R2A7mB0F6C7GH0F0FcY7QC0g9HXAH2N0T2A7mH0DUDfYHQfoPsYfQvQtxh9B9B3GD0A6AFGDwF6iNEuQLsY7QG0h9EjgB5h9BigxxjtA7SP0ROAnlzzEsqjZkgAb5UKng3mBtCoEKDNJeURMGkpWsejkCazfJ/NKGpuXHevSOx5bAPUxqgDUAejQ4AOMUoBSjE6AugIoy5AXYx6APUwygDKMPoeoO8xeg7Qc4z6APUxGgA0wGgI0BCj9bdUoRFGY4DGGP0A0A8Y5QDlGE0AmmBUAFRgNAVoitExQMcYvQDoBUYnAJ1gdArQKUYvAXp5zcSCZSATvsyK87Ug87pEZpyxWMrsqgli8qxI6jxpptK1mrpRUTc0dauibmnqTkXd0dTdirqrqXsVdU9TDyrqgaYeV9RjTe1X1H4xRB4RyffLmJcnnp46KmRpVhe3F+K2Ji5OKq96OtWgQ4+KBVM8aE66CyddXewtxJ4uHi3EI030l8LzcXiiGp6A4eXLJNdlSROnC3Gqi5cL8VIT+6XW15STUjnRlKS/6O/VxFZffj+6wC+/Wr+Ox3I2vwC5nNLzZcgmfuypwZBAeX2yiqrCRRRQs7zwOfPr1FIDLJ6drsv7l09HQg546PrUbLbXrLXmusWZ6wmL55W1bm1N4srlzpYLLG/htNkurM5q/GY0LvxEcqUTEXF1+81U7dyu4lI35hxay+pbmPcIL2Jdsla1N8e8zyO7cFt2cn9ucI0j++puTF0WZuqZs8lMOqBSnz/WrIbDSeFlJC/dcm9U3wuILydhdvUwGWTN9VndknCZJ04Kj2k4lPd1KrLcbqmnJYasWXgraxZq1rKO/a+tgoI00I3J5BbGEkLGiTqDBZ2ILEnt99QR6lNGHRJyLCmY9aI+n8ZH83l/nC8V9enFJlOaMBKaLCw/Fy23GnMWqbyCe9Gg1nDMtUBzenotvqZtPrnB5fUG2obks3NMK0F7z5xI5RnbRD4P8tS77j7KhxY5jxKtOafAnduxTJHq3K/tjm65ObravpknD/m+qbKFWnte0WAFqBEujWVW5w7kFYfLIvOjsN5bliPy/w2QU1LKVQ3UelI0V3Tmhia9ueN56De59yr+Ia+d72XDnbrSydvp3BRY5yquzk1RTQRP1WVsLHelYiHmFerEGaw02/VPpHqht/6k3XrSfttqPv2x/Hx6z/jO+MF4ZLSNn4ynxktj3+gajjE1fjV+M35f/WP1z9W/V/8p0Lt3SpsHxtJv9d//AHoWx3o=</latexit> <latexit sha1_base64="OCKIFR8Z4i9tsF1/wXrUpjAecow=">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</latexit>

    <latexit 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<latexit sha1_base64="OCKIFR8Z4i9tsF1/wXrUpjAecow=">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</latexit> yi = g ( xi, ! ) <latexit 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<latexit 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<latexit 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<latexit 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(x, x 0 ; ✓) = exp( | x x 0|2 /✓) <latexit 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<latexit 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<latexit 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<latexit 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Gaussian process regression { xi, yi } pairs GIVEN ASSUME one realization of a GP among many possible realizations CORRELATION MODEL (e.g.) FIT x y PREDICT (B.L.U.E.) y ( x ) = E[ g ( x, ·) | { xi, yi } ] = X i yi wi( x ) <latexit sha1_base64="ZyiY2DW+riZWoS77N2LOZspi1oc=">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</latexit> <latexit sha1_base64="ZyiY2DW+riZWoS77N2LOZspi1oc=">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</latexit> <latexit 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<latexit sha1_base64="ZyiY2DW+riZWoS77N2LOZspi1oc=">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</latexit> maximize ✓ likelihood(✓; { xi, yi } ) <latexit 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<latexit 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<latexit 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<latexit 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  40. yi = g ( xi, ·) <latexit sha1_base64="OCKIFR8Z4i9tsF1/wXrUpjAecow=">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</latexit> <latexit sha1_base64="OCKIFR8Z4i9tsF1/wXrUpjAecow=">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</latexit>

    <latexit 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<latexit sha1_base64="OCKIFR8Z4i9tsF1/wXrUpjAecow=">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</latexit> yi = g ( xi, ! ) <latexit 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<latexit 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<latexit 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<latexit 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(x, x 0 ; ✓) = exp( | x x 0|2 /✓) <latexit 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<latexit 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<latexit 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<latexit sha1_base64="mhSFZPmMH7gb/9CDUANsuLrOqX8=">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</latexit> Gaussian process regression { xi, yi } pairs GIVEN ASSUME one realization of a GP among many possible realizations CORRELATION MODEL (e.g.) FIT x y maximize ✓ likelihood(✓; { xi, yi } ) <latexit sha1_base64="6TzVNyNn1NL/ui9Twe085y85hiQ=">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</latexit> <latexit 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<latexit sha1_base64="6TzVNyNn1NL/ui9Twe085y85hiQ=">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</latexit> <latexit sha1_base64="6TzVNyNn1NL/ui9Twe085y85hiQ=">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</latexit> PREDICT (B.L.U.E.) y ( x ) = E[ g ( x, ·) | { xi, yi } ] = X i yi wi( x ) <latexit sha1_base64="ZyiY2DW+riZWoS77N2LOZspi1oc=">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</latexit> <latexit sha1_base64="ZyiY2DW+riZWoS77N2LOZspi1oc=">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</latexit> <latexit sha1_base64="ZyiY2DW+riZWoS77N2LOZspi1oc=">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</latexit> <latexit sha1_base64="ZyiY2DW+riZWoS77N2LOZspi1oc=">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</latexit> QUANTIFY UNCERTAINTY V ar[ g(x, · ) | { xi, yi } ] = “formula” <latexit 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<latexit 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<latexit 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<latexit 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  41. yi = g ( xi, ·) <latexit sha1_base64="OCKIFR8Z4i9tsF1/wXrUpjAecow=">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</latexit> <latexit sha1_base64="OCKIFR8Z4i9tsF1/wXrUpjAecow=">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</latexit>

    <latexit sha1_base64="OCKIFR8Z4i9tsF1/wXrUpjAecow=">AAAWLHicjZhNb9s2GMfV7q3z3tIVOe2izSjQAkFh57DtMqBNmqZJ3TRtYidOFBiUTEts9FaKcuwI/iy7bpd9ml2GYdd9jpGS7MjiP1kMBKH4/z18HpIi+VB27LNEtFp/3bn70ceffPrZvc8bX3z51dffrNz/tpdEKXdo14n8iB/bJKE+C2lXMOHT45hTEtg+PbLPN5V+NKY8YVF4KKYxPQuIG7IRc4iQVYOVB9MBM38x3UeTAVszLWcYiceDlWbrSSv/mXqhXRaaRvnbH9xfvWMNIycNaCgcnyTJabsVi7OMcMEcn84aVprQmDjnxKWnshiSgCZnWR79zHwoa4bmKOLyLxRmXlu1yEiQJNPAlmRAhJfUNVWJtNNUjH4+y1gYp4KGTuFolPqmiEw1FOaQceoIfyoLxOFMxmo6HuHEEXLAGg0r5tGYDakTBQEJh5klPcxO22eZZUf+UEUU+VmzPZs9bFichvRiAY6pU4AqJnuUQw2rRhAft9ZoPDQ3Cy6RRaWaaRxTbjpynvWo6JTOck/ZjvKiBf1MqjRMUk5VNAX5bAbRDYBuYHQToJsYfQ7Q5xjdAugWRl8A9AVGtwG6jdGXAH2J0R2A7mB0F6C7GH0F0FcY7QC0g9HXAH2N0T2A7mH0DUDfYHQfoPsYfQvQtxh9B9B3GD0A6AFGDwF6iNEuQLsY7QG0h9EjgB5h9BigxxjtA7SP0ROAnlzzEsqjZkgAb5UKng3mBtCoEKDNJeURMGkpWsejkCazfJ/NKGpuXHevSOx5bAPUxqgDUAejQ4AOMUoBSjE6AugIoy5AXYx6APUwygDKMPoeoO8xeg7Qc4z6APUxGgA0wGgI0BCj9bdUoRFGY4DGGP0A0A8Y5QDlGE0AmmBUAFRgNAVoitExQMcYvQDoBUYnAJ1gdArQKUYvAXp5zcSCZSATvsyK87Ug87pEZpyxWMrsqgli8qxI6jxpptK1mrpRUTc0dauibmnqTkXd0dTdirqrqXsVdU9TDyrqgaYeV9RjTe1X1H4xRB4RyffLmJcnnp46KmRpVhe3F+K2Ji5OKq96OtWgQ4+KBVM8aE66CyddXewtxJ4uHi3EI030l8LzcXiiGp6A4eXLJNdlSROnC3Gqi5cL8VIT+6XW15STUjnRlKS/6O/VxFZffj+6wC+/Wr+Ox3I2vwC5nNLzZcgmfuypwZBAeX2yiqrCRRRQs7zwOfPr1FIDLJ6drsv7l09HQg546PrUbLbXrLXmusWZ6wmL55W1bm1N4srlzpYLLG/htNkurM5q/GY0LvxEcqUTEXF1+81U7dyu4lI35hxay+pbmPcIL2Jdsla1N8e8zyO7cFt2cn9ucI0j++puTF0WZuqZs8lMOqBSnz/WrIbDSeFlJC/dcm9U3wuILydhdvUwGWTN9VndknCZJ04Kj2k4lPd1KrLcbqmnJYasWXgraxZq1rKO/a+tgoI00I3J5BbGEkLGiTqDBZ2ILEnt99QR6lNGHRJyLCmY9aI+n8ZH83l/nC8V9enFJlOaMBKaLCw/Fy23GnMWqbyCe9Gg1nDMtUBzenotvqZtPrnB5fUG2obks3NMK0F7z5xI5RnbRD4P8tS77j7KhxY5jxKtOafAnduxTJHq3K/tjm65ObravpknD/m+qbKFWnte0WAFqBEujWVW5w7kFYfLIvOjsN5bliPy/w2QU1LKVQ3UelI0V3Tmhia9ueN56De59yr+Ia+d72XDnbrSydvp3BRY5yquzk1RTQRP1WVsLHelYiHmFerEGaw02/VPpHqht/6k3XrSfttqPv2x/Hx6z/jO+MF4ZLSNn4ynxktj3+gajjE1fjV+M35f/WP1z9W/V/8p0Lt3SpsHxtJv9d//AHoWx3o=</latexit> <latexit sha1_base64="OCKIFR8Z4i9tsF1/wXrUpjAecow=">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</latexit> yi = g ( xi, ! ) <latexit 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<latexit 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<latexit 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<latexit 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(x, x 0 ; ✓) = exp( | x x 0|2 /✓) <latexit 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<latexit 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<latexit 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<latexit sha1_base64="mhSFZPmMH7gb/9CDUANsuLrOqX8=">AAAWbHicjZhbb9s2FMfVXTvvlm5rXooB2oyuKZB1dh62AcWANmmaJnXTtLknygxKpi02upWiHTmqPtg+yp72ur3sM4yUZEcW/8liIAjF/+/wHFIieUg78lgsWq0/b7z3/gcffvTxzU8an372+Rdfzt36ai8Oh9yhu07ohfzAJjH1WEB3BRMePYg4Jb7t0X37dEXp+yPKYxYGO2Ic0ROfDALWZw4Rsqo7t22dkigiC8licu+htWgJmoi81ZTTXpZawqWCZPdN6+Fv1kPTokm08C75Mbn37velny6Du3PN1oNW/jP1QrssNI3yt9W9dfuG1QudoU8D4Xgkjo/brUicpIQL5ng0a1jDmEbEOSUDeiyLAfFpfJLmrjPzrqzpmf2Qy79AmHlt1SIlfhyPfVuSPhFuXNdUJdKOh6L/60nKgmgoaOAUjvpDzxShqYbS7DFOHeGNZYE4nMlYTcclnDhCDnijYUU8HLEedULfJ0EvtaSH7Lh9klp26PVURKGXNttZdrdhcRrQsyk4ok4Bqpjsfg41rBpBPNxao3HXXCm4WBaVag6jiHLTkd+JHhUd0yz3lK4rL1rQj6VKg3jIqYqmIB9nEF0G6DJGVwC6gtEnAH2C0VWArmL0KUCfYnQNoGsYfQbQZxhdB+g6RjcAuoHR5wB9jtEOQDsYfQHQFxjdBOgmRl8C9CVGtwC6hdFXAH2F0dcAfY3RbYBuY3QHoDsY3QXoLkb3ALqH0X2A7mP0AKAHGD0E6CFGjwB6dMlHKLeqHgG8VSr4bbCBD40KAdqcUx4Ck5aidTwMaJzl62xKUXOjuntFYs8jG6A2Rh2AOhjtAbSHUQpQitE+QPsYHQB0gFEXoC5GGUAZRt8A9A1GTwF6ilEPoB5GfYD6GA0AGmC0/pUqNMRoBNAIo28B+hajHKAcozFAY4wKgAqMDgE6xOgIoCOMngH0DKMJQBOMjgE6xug5QM8vebFgGsiEL7WifC7IvC6WGWckZjK7aoIYPy6SOleaqXStpi5X1GVNXa2oq5q6XlHXNXWjom5o6mZF3dTU7Yq6rakHFfVAUw8r6mExRC4R8XezmJsnnq7aKmQpq4trU3FNE6c7lVvdnWrQTn4CKpniQXOyO3Wyq4t7U3FPF/en4r4mejPheTg8UQ1PwPDyaZLrsqSJ46k41sXzqXiuiYeldqgpR6VypCnx4bS/Fy+2+vF74Rn++NX8dVyWs/kBaMApPZ2FbOJFrhoMCZTHJ6uoKlyEPjXLA58zOU7NNMCi7HhJnr882hdywIOBR81me9FabC5ZnA1cYfG8stat1SSqHO5sOcHyFo6b7cLqpMavhKPCTyhnOhEhV6ffVNVO7CoudWPOobWsvob5HuFFrDPWqvbqmLd4aBduy05uTQwucWRfnI3pgAWpeuYsyaQDKvXJY82q10sKL3156JZro7ovIJ58CdnFQ9JNm0tZ3ZJwmScmhcdh0JPndSrS3G6mpyWGrFlwLWsWaNayjv2vrYL8oa8bk+QaxhJCxrHag9WlTRoP7TfUEeoqow4JOZYUvPWiPn+NC5P3fj+fKurqxSZjGjMSmCwor5tmW404C1Vewd2wW2s44lqgOT2+FF/UFp/c4PxyA21B8tgpppWgfWdOqPKMNSKfu3nqXXcf5kOLnIex1pxT4M71WKZIte/XVsdBuTgOtHUzTx7ydVNlC7X23KLBClAjBjSSWd2gK484XBaZFwb13rIckf+vgJySUq5qoNaTormiM1c06U4cT0K/yr1b8Q95bX8vG+7UlU7eTueqwDoXcXWuiioRfKgOYyO5KhUTMa9QO053rtmuX5Hqhb2lB+3Wg/arVvPRz+X16U3jjvG9sWC0jV+MR8YzY8vYNRzjD+Mv42/jn9v/zn8zf2f+2wJ970Zp87Ux85v/4T9h5t8Q</latexit> Gaussian process regression { xi, yi } pairs GIVEN ASSUME one realization of a GP among many possible realizations CORRELATION MODEL (e.g.) FIT x y maximize ✓ likelihood(✓; { xi, yi } ) <latexit sha1_base64="6TzVNyNn1NL/ui9Twe085y85hiQ=">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</latexit> <latexit 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<latexit sha1_base64="6TzVNyNn1NL/ui9Twe085y85hiQ=">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</latexit> <latexit sha1_base64="6TzVNyNn1NL/ui9Twe085y85hiQ=">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</latexit> PREDICT (B.L.U.E.) y ( x ) = E[ g ( x, ·) | { xi, yi } ] = X i yi wi( x ) <latexit sha1_base64="ZyiY2DW+riZWoS77N2LOZspi1oc=">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</latexit> <latexit sha1_base64="ZyiY2DW+riZWoS77N2LOZspi1oc=">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</latexit> <latexit sha1_base64="ZyiY2DW+riZWoS77N2LOZspi1oc=">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</latexit> <latexit sha1_base64="ZyiY2DW+riZWoS77N2LOZspi1oc=">AAAWY3icjZhdb9s2FIbV7qtztzXt1twMA7QZHVLAKOxg2HYzoE2apknTNG1iJ45lGJJMW2z0VYpy7Gj6T/s1A3a13ex/jJRkRxbfZDEQhOL7HJ5DUiQPZYUujXiz+det2x99/Mmnn935vHb3iy+/urdy/0EnCmJmk7YduAE7scyIuNQnbU65S05CRkzPcsmxdbYp9eMJYREN/CM+C0nfM8c+HVHb5KJqsLI7W5s+1n/8TTc8kzuWlWylPaMxXps2DHsY8MdG43ejYSTTAW3MBtRIjUbfMGqSj2JvQHVZ2TgfUNHKYKXefNLMfrpaaBWFulb8Dgb3H94yhoEde8TntmtGUa/VDHk/MRmntkvSmhFHJDTtM3NMeqLomx6J+knW6VR/JGqG+ihg4s/nelZbtkhML4pmniVI2bWoqslKpPViPvq1n1A/jDnx7dzRKHZ1HuhyBPUhZcTm7kwUTJtREatuOyYzbS7GuVYzQhZM6JDYgeeZ/jCRA5v2Wv3EsAJ3KCMK3KTeStNHNYMRn5wvwAmxczCbilEG1YwKYbq4tVrtkb6Zc5EoSlWPw5Aw3RavhxoVmZE085TsSC9K0M+ESvwoZkRGk5PPUohuAHQDo5sA3cToc4A+x+gWQLcw+gKgLzC6DdBtjL4E6EuM7gB0B6O7AN3F6CuAvsLoHkD3MPoaoK8xug/QfYy+AegbjB4A9ACjbwH6FqPvAPoOo4cAPcToEUCPMNoGaBujHYB2MHoM0GOMngD0BKNdgHYxegrQ0yteQnFCDU3AG4WCZ4OOPWiUC9DmgrAAmDQlreKBT6I022cTgpqbVN1LEnueWAC1MGoD1MboEKBDjBKAEoyOADrC6BigY4w6AHUwSgFKMfoeoO8xegbQM4y6AHUx6gHUw6gPUB+j1bdUogFGQ4CGGP0A0A8YZQBlGI0AGmGUA5RjNAZojNEJQCcYPQfoOUanAJ1idAbQGUYvAHpxxcSCZSASvsQIs7Ug8rpIZJwhX8rsygli9CxP6hxhJtO1irpRUjcUdaukbinqTkndUdTdkrqrqPsldV9RD0vqoaKelNQTRe2W1G4+RI7Jo++XMSdLPB15VIhSWhW3F+K2Ii5OKqd8OlWgI4fwBZM/KE7aCydtVewsxI4qHi/EY0V0l8JzcXi8HB6H4WXLJNNFSRFnC3GmihcL8UIRu4XWVZTTQjlVlKi76O/lxJZffjc4xy+/XL+2QzM2uwCNGSFny5BluqEjB0MAxfXJyKtyF4FH9OLCZ8+vU0sN0DDtrYv7l0tGXAy4P3aJXm81jEZ93WB07HCDZZWVbm1Nw9LlTt6zsxZ69VZu1a/wm8Ek9xOIlW7ygMnbbyJr53Yll6oxY9BaVN/AvGOyPNYla1l7fcwHLLByt0UnD+YGVziyLu/GZEz9RD4zOk2FAyL0+WPFajic5l5G4tIt9kb5vcB0xSSklw/TQVJfT6uWJhN54jT3GPtDcV8nPMnslnpaYMia+jeypr5iLero/9pKyIs91dic3sBYQMg4kmcwJ1OeRLH1nthcfsqoQlyMJQGzntdn07g2n/fH2VKRn14sc0Yiavo69YuvTMuthowGMq9gTjCoNBwyJdCMnl2JN5TNJzO4uNpA2ZBceoZpKSjvmR3IPGPbFM+DLPWuug+yoUXOg0hpzs5x+2YslaQ89yu747jYHMfKvpklD9m+KbOFSntO3mAJqBBjEoqsbjwQVxwmitQN/GpvaYaI/9dAdkFJVxVQ6UneXN6Za5p05o7noV/n3in5h7xyvhcN71WVvaydvesC27uMa++6qKacxfIyNhG7Ur4Qswp54gxW6q3qJ1K10Fl/0mo+ab39qf705+Lz6R3tW+0HbU1rab9oT7WX2oHW1mztD+1P7W/tn4f/rt5dfbD6TY7evlXYfK0t/Va/+w+KbdhO</latexit> QUANTIFY UNCERTAINTY V ar[ g(x, · ) | { xi, yi } ] = “formula” <latexit 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<latexit 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<latexit 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<latexit 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  42. yi = g ( xi, ·) <latexit sha1_base64="OCKIFR8Z4i9tsF1/wXrUpjAecow=">AAAWLHicjZhNb9s2GMfV7q3z3tIVOe2izSjQAkFh57DtMqBNmqZJ3TRtYidOFBiUTEts9FaKcuwI/iy7bpd9ml2GYdd9jpGS7MjiP1kMBKH4/z18HpIi+VB27LNEtFp/3bn70ceffPrZvc8bX3z51dffrNz/tpdEKXdo14n8iB/bJKE+C2lXMOHT45hTEtg+PbLPN5V+NKY8YVF4KKYxPQuIG7IRc4iQVYOVB9MBM38x3UeTAVszLWcYiceDlWbrSSv/mXqhXRaaRvnbH9xfvWMNIycNaCgcnyTJabsVi7OMcMEcn84aVprQmDjnxKWnshiSgCZnWR79zHwoa4bmKOLyLxRmXlu1yEiQJNPAlmRAhJfUNVWJtNNUjH4+y1gYp4KGTuFolPqmiEw1FOaQceoIfyoLxOFMxmo6HuHEEXLAGg0r5tGYDakTBQEJh5klPcxO22eZZUf+UEUU+VmzPZs9bFichvRiAY6pU4AqJnuUQw2rRhAft9ZoPDQ3Cy6RRaWaaRxTbjpynvWo6JTOck/ZjvKiBf1MqjRMUk5VNAX5bAbRDYBuYHQToJsYfQ7Q5xjdAugWRl8A9AVGtwG6jdGXAH2J0R2A7mB0F6C7GH0F0FcY7QC0g9HXAH2N0T2A7mH0DUDfYHQfoPsYfQvQtxh9B9B3GD0A6AFGDwF6iNEuQLsY7QG0h9EjgB5h9BigxxjtA7SP0ROAnlzzEsqjZkgAb5UKng3mBtCoEKDNJeURMGkpWsejkCazfJ/NKGpuXHevSOx5bAPUxqgDUAejQ4AOMUoBSjE6AugIoy5AXYx6APUwygDKMPoeoO8xeg7Qc4z6APUxGgA0wGgI0BCj9bdUoRFGY4DGGP0A0A8Y5QDlGE0AmmBUAFRgNAVoitExQMcYvQDoBUYnAJ1gdArQKUYvAXp5zcSCZSATvsyK87Ug87pEZpyxWMrsqgli8qxI6jxpptK1mrpRUTc0dauibmnqTkXd0dTdirqrqXsVdU9TDyrqgaYeV9RjTe1X1H4xRB4RyffLmJcnnp46KmRpVhe3F+K2Ji5OKq96OtWgQ4+KBVM8aE66CyddXewtxJ4uHi3EI030l8LzcXiiGp6A4eXLJNdlSROnC3Gqi5cL8VIT+6XW15STUjnRlKS/6O/VxFZffj+6wC+/Wr+Ox3I2vwC5nNLzZcgmfuypwZBAeX2yiqrCRRRQs7zwOfPr1FIDLJ6drsv7l09HQg546PrUbLbXrLXmusWZ6wmL55W1bm1N4srlzpYLLG/htNkurM5q/GY0LvxEcqUTEXF1+81U7dyu4lI35hxay+pbmPcIL2Jdsla1N8e8zyO7cFt2cn9ucI0j++puTF0WZuqZs8lMOqBSnz/WrIbDSeFlJC/dcm9U3wuILydhdvUwGWTN9VndknCZJ04Kj2k4lPd1KrLcbqmnJYasWXgraxZq1rKO/a+tgoI00I3J5BbGEkLGiTqDBZ2ILEnt99QR6lNGHRJyLCmY9aI+n8ZH83l/nC8V9enFJlOaMBKaLCw/Fy23GnMWqbyCe9Gg1nDMtUBzenotvqZtPrnB5fUG2obks3NMK0F7z5xI5RnbRD4P8tS77j7KhxY5jxKtOafAnduxTJHq3K/tjm65ObravpknD/m+qbKFWnte0WAFqBEujWVW5w7kFYfLIvOjsN5bliPy/w2QU1LKVQ3UelI0V3Tmhia9ueN56De59yr+Ia+d72XDnbrSydvp3BRY5yquzk1RTQRP1WVsLHelYiHmFerEGaw02/VPpHqht/6k3XrSfttqPv2x/Hx6z/jO+MF4ZLSNn4ynxktj3+gajjE1fjV+M35f/WP1z9W/V/8p0Lt3SpsHxtJv9d//AHoWx3o=</latexit> <latexit sha1_base64="OCKIFR8Z4i9tsF1/wXrUpjAecow=">AAAWLHicjZhNb9s2GMfV7q3z3tIVOe2izSjQAkFh57DtMqBNmqZJ3TRtYidOFBiUTEts9FaKcuwI/iy7bpd9ml2GYdd9jpGS7MjiP1kMBKH4/z18HpIi+VB27LNEtFp/3bn70ceffPrZvc8bX3z51dffrNz/tpdEKXdo14n8iB/bJKE+C2lXMOHT45hTEtg+PbLPN5V+NKY8YVF4KKYxPQuIG7IRc4iQVYOVB9MBM38x3UeTAVszLWcYiceDlWbrSSv/mXqhXRaaRvnbH9xfvWMNIycNaCgcnyTJabsVi7OMcMEcn84aVprQmDjnxKWnshiSgCZnWR79zHwoa4bmKOLyLxRmXlu1yEiQJNPAlmRAhJfUNVWJtNNUjH4+y1gYp4KGTuFolPqmiEw1FOaQceoIfyoLxOFMxmo6HuHEEXLAGg0r5tGYDakTBQEJh5klPcxO22eZZUf+UEUU+VmzPZs9bFichvRiAY6pU4AqJnuUQw2rRhAft9ZoPDQ3Cy6RRaWaaRxTbjpynvWo6JTOck/ZjvKiBf1MqjRMUk5VNAX5bAbRDYBuYHQToJsYfQ7Q5xjdAugWRl8A9AVGtwG6jdGXAH2J0R2A7mB0F6C7GH0F0FcY7QC0g9HXAH2N0T2A7mH0DUDfYHQfoPsYfQvQtxh9B9B3GD0A6AFGDwF6iNEuQLsY7QG0h9EjgB5h9BigxxjtA7SP0ROAnlzzEsqjZkgAb5UKng3mBtCoEKDNJeURMGkpWsejkCazfJ/NKGpuXHevSOx5bAPUxqgDUAejQ4AOMUoBSjE6AugIoy5AXYx6APUwygDKMPoeoO8xeg7Qc4z6APUxGgA0wGgI0BCj9bdUoRFGY4DGGP0A0A8Y5QDlGE0AmmBUAFRgNAVoitExQMcYvQDoBUYnAJ1gdArQKUYvAXp5zcSCZSATvsyK87Ug87pEZpyxWMrsqgli8qxI6jxpptK1mrpRUTc0dauibmnqTkXd0dTdirqrqXsVdU9TDyrqgaYeV9RjTe1X1H4xRB4RyffLmJcnnp46KmRpVhe3F+K2Ji5OKq96OtWgQ4+KBVM8aE66CyddXewtxJ4uHi3EI030l8LzcXiiGp6A4eXLJNdlSROnC3Gqi5cL8VIT+6XW15STUjnRlKS/6O/VxFZffj+6wC+/Wr+Ox3I2vwC5nNLzZcgmfuypwZBAeX2yiqrCRRRQs7zwOfPr1FIDLJ6drsv7l09HQg546PrUbLbXrLXmusWZ6wmL55W1bm1N4srlzpYLLG/htNkurM5q/GY0LvxEcqUTEXF1+81U7dyu4lI35hxay+pbmPcIL2Jdsla1N8e8zyO7cFt2cn9ucI0j++puTF0WZuqZs8lMOqBSnz/WrIbDSeFlJC/dcm9U3wuILydhdvUwGWTN9VndknCZJ04Kj2k4lPd1KrLcbqmnJYasWXgraxZq1rKO/a+tgoI00I3J5BbGEkLGiTqDBZ2ILEnt99QR6lNGHRJyLCmY9aI+n8ZH83l/nC8V9enFJlOaMBKaLCw/Fy23GnMWqbyCe9Gg1nDMtUBzenotvqZtPrnB5fUG2obks3NMK0F7z5xI5RnbRD4P8tS77j7KhxY5jxKtOafAnduxTJHq3K/tjm65ObravpknD/m+qbKFWnte0WAFqBEujWVW5w7kFYfLIvOjsN5bliPy/w2QU1LKVQ3UelI0V3Tmhia9ueN56De59yr+Ia+d72XDnbrSydvp3BRY5yquzk1RTQRP1WVsLHelYiHmFerEGaw02/VPpHqht/6k3XrSfttqPv2x/Hx6z/jO+MF4ZLSNn4ynxktj3+gajjE1fjV+M35f/WP1z9W/V/8p0Lt3SpsHxtJv9d//AHoWx3o=</latexit>

    <latexit sha1_base64="OCKIFR8Z4i9tsF1/wXrUpjAecow=">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</latexit> <latexit sha1_base64="OCKIFR8Z4i9tsF1/wXrUpjAecow=">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</latexit> yi = g ( xi, ! ) <latexit 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<latexit 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<latexit 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<latexit 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(x, x 0 ; ✓) = exp( | x x 0|2 /✓) <latexit 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<latexit 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<latexit 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<latexit sha1_base64="mhSFZPmMH7gb/9CDUANsuLrOqX8=">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</latexit> Gaussian process regression { xi, yi } pairs GIVEN ASSUME one realization of a GP among many possible realizations CORRELATION MODEL (e.g.) FIT x y maximize ✓ likelihood(✓; { xi, yi } ) <latexit sha1_base64="6TzVNyNn1NL/ui9Twe085y85hiQ=">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</latexit> <latexit 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<latexit sha1_base64="6TzVNyNn1NL/ui9Twe085y85hiQ=">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</latexit> <latexit sha1_base64="6TzVNyNn1NL/ui9Twe085y85hiQ=">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</latexit> PREDICT (B.L.U.E.) y ( x ) = E[ g ( x, ·) | { xi, yi } ] = X i yi wi( x ) <latexit sha1_base64="ZyiY2DW+riZWoS77N2LOZspi1oc=">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</latexit> <latexit sha1_base64="ZyiY2DW+riZWoS77N2LOZspi1oc=">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</latexit> <latexit sha1_base64="ZyiY2DW+riZWoS77N2LOZspi1oc=">AAAWY3icjZhdb9s2FIbV7qtztzXt1twMA7QZHVLAKOxg2HYzoE2apknTNG1iJ45lGJJMW2z0VYpy7Gj6T/s1A3a13ex/jJRkRxbfZDEQhOL7HJ5DUiQPZYUujXiz+det2x99/Mmnn935vHb3iy+/urdy/0EnCmJmk7YduAE7scyIuNQnbU65S05CRkzPcsmxdbYp9eMJYREN/CM+C0nfM8c+HVHb5KJqsLI7W5s+1n/8TTc8kzuWlWylPaMxXps2DHsY8MdG43ejYSTTAW3MBtRIjUbfMGqSj2JvQHVZ2TgfUNHKYKXefNLMfrpaaBWFulb8Dgb3H94yhoEde8TntmtGUa/VDHk/MRmntkvSmhFHJDTtM3NMeqLomx6J+knW6VR/JGqG+ihg4s/nelZbtkhML4pmniVI2bWoqslKpPViPvq1n1A/jDnx7dzRKHZ1HuhyBPUhZcTm7kwUTJtREatuOyYzbS7GuVYzQhZM6JDYgeeZ/jCRA5v2Wv3EsAJ3KCMK3KTeStNHNYMRn5wvwAmxczCbilEG1YwKYbq4tVrtkb6Zc5EoSlWPw5Aw3RavhxoVmZE085TsSC9K0M+ESvwoZkRGk5PPUohuAHQDo5sA3cToc4A+x+gWQLcw+gKgLzC6DdBtjL4E6EuM7gB0B6O7AN3F6CuAvsLoHkD3MPoaoK8xug/QfYy+AegbjB4A9ACjbwH6FqPvAPoOo4cAPcToEUCPMNoGaBujHYB2MHoM0GOMngD0BKNdgHYxegrQ0yteQnFCDU3AG4WCZ4OOPWiUC9DmgrAAmDQlreKBT6I022cTgpqbVN1LEnueWAC1MGoD1MboEKBDjBKAEoyOADrC6BigY4w6AHUwSgFKMfoeoO8xegbQM4y6AHUx6gHUw6gPUB+j1bdUogFGQ4CGGP0A0A8YZQBlGI0AGmGUA5RjNAZojNEJQCcYPQfoOUanAJ1idAbQGUYvAHpxxcSCZSASvsQIs7Ug8rpIZJwhX8rsygli9CxP6hxhJtO1irpRUjcUdaukbinqTkndUdTdkrqrqPsldV9RD0vqoaKelNQTRe2W1G4+RI7Jo++XMSdLPB15VIhSWhW3F+K2Ii5OKqd8OlWgI4fwBZM/KE7aCydtVewsxI4qHi/EY0V0l8JzcXi8HB6H4WXLJNNFSRFnC3GmihcL8UIRu4XWVZTTQjlVlKi76O/lxJZffjc4xy+/XL+2QzM2uwCNGSFny5BluqEjB0MAxfXJyKtyF4FH9OLCZ8+vU0sN0DDtrYv7l0tGXAy4P3aJXm81jEZ93WB07HCDZZWVbm1Nw9LlTt6zsxZ69VZu1a/wm8Ek9xOIlW7ygMnbbyJr53Yll6oxY9BaVN/AvGOyPNYla1l7fcwHLLByt0UnD+YGVziyLu/GZEz9RD4zOk2FAyL0+WPFajic5l5G4tIt9kb5vcB0xSSklw/TQVJfT6uWJhN54jT3GPtDcV8nPMnslnpaYMia+jeypr5iLero/9pKyIs91dic3sBYQMg4kmcwJ1OeRLH1nthcfsqoQlyMJQGzntdn07g2n/fH2VKRn14sc0Yiavo69YuvTMuthowGMq9gTjCoNBwyJdCMnl2JN5TNJzO4uNpA2ZBceoZpKSjvmR3IPGPbFM+DLPWuug+yoUXOg0hpzs5x+2YslaQ89yu747jYHMfKvpklD9m+KbOFSntO3mAJqBBjEoqsbjwQVxwmitQN/GpvaYaI/9dAdkFJVxVQ6UneXN6Za5p05o7noV/n3in5h7xyvhcN71WVvaydvesC27uMa++6qKacxfIyNhG7Ur4Qswp54gxW6q3qJ1K10Fl/0mo+ab39qf705+Lz6R3tW+0HbU1rab9oT7WX2oHW1mztD+1P7W/tn4f/rt5dfbD6TY7evlXYfK0t/Va/+w+KbdhO</latexit> <latexit sha1_base64="ZyiY2DW+riZWoS77N2LOZspi1oc=">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</latexit> QUANTIFY UNCERTAINTY V ar[ g(x, · ) | { xi, yi } ] = “formula” <latexit 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<latexit 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<latexit 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<latexit 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  43. Gaussian process regression Radial basis approximation x y x y

  44. Radial basis approximation x y GIVEN a queryable function f

    ( x )
  45. Radial basis approximation x y a queryable function GIVEN f

    ( x ) centers x1, . . . , xn <latexit 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<latexit 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<latexit 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<latexit 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  46. the error is small ks fk <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit>

    <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> find such that s ( x ) <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> Radial basis approximation x y a queryable function GIVEN f ( x ) centers x1, . . . , xn <latexit 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<latexit 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<latexit 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<latexit sha1_base64="FqyAIE90iFEsMkh76qjqpRo5BVw=">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</latexit> GOAL
  47. the error is small ks fk <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit>

    <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> find such that s ( x ) <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> Radial basis approximation x y a queryable function GIVEN f ( x ) centers x1, . . . , xn <latexit 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<latexit 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<latexit sha1_base64="FqyAIE90iFEsMkh76qjqpRo5BVw=">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</latexit> <latexit sha1_base64="FqyAIE90iFEsMkh76qjqpRo5BVw=">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</latexit> GOAL QUERY THE FUNCTION yi = f ( xi) <latexit 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<latexit 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<latexit 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<latexit 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  48. the error is small ks fk <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit>

    <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> find such that s ( x ) <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> Radial basis approximation a queryable function GIVEN f ( x ) centers x1, . . . , xn <latexit 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<latexit 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<latexit sha1_base64="FqyAIE90iFEsMkh76qjqpRo5BVw=">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</latexit> <latexit sha1_base64="FqyAIE90iFEsMkh76qjqpRo5BVw=">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</latexit> GOAL QUERY THE FUNCTION yi = f ( xi) <latexit 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<latexit 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<latexit 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<latexit sha1_base64="DSMIHsDlFYUZwiwOabLZEBLNT+s=">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</latexit> CHOOSE KERNEL (x, x 0 ; ") = exp(" | x x 0|2 ) <latexit 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<latexit 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<latexit 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<latexit 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x y
  49. the error is small ks fk <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit>

    <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> find such that s ( x ) <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> Radial basis approximation a queryable function GIVEN f ( x ) centers x1, . . . , xn <latexit 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<latexit 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<latexit sha1_base64="FqyAIE90iFEsMkh76qjqpRo5BVw=">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</latexit> <latexit sha1_base64="FqyAIE90iFEsMkh76qjqpRo5BVw=">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</latexit> GOAL QUERY THE FUNCTION yi = f ( xi) <latexit 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<latexit 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<latexit 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<latexit sha1_base64="DSMIHsDlFYUZwiwOabLZEBLNT+s=">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</latexit> CHOOSE KERNEL (x, x 0 ; ") = exp(" | x x 0|2 ) <latexit sha1_base64="HvFcm2PJ26lSUDpyVkXpnM24lRc=">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</latexit> <latexit sha1_base64="HvFcm2PJ26lSUDpyVkXpnM24lRc=">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</latexit> <latexit sha1_base64="HvFcm2PJ26lSUDpyVkXpnM24lRc=">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</latexit> <latexit 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x y DEFINES BASIS i( x ) =  ( x, xi; " ) <latexit 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  50. the error is small ks fk <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">AAAWHnicjZjLcts2FIbp9Jaqt6Qdr7phq8lMOpNmJC/aLhM7ji9RHCe2JMumRwNSkIiIt4CgLJnRQ3Tbbvo03XW6bd+mAEnJFPHbtWY8BvF/B+eAIIAD2JHHYtFo/Lt254MPP/r4k7uf1j77/Isvv7p3/+tOHCbcoW0n9EJ+YpOYeiygbcGER08iTolve7Rrj7eU3p1QHrMwOBaziJ77ZBSwIXOIkFVd633849B6379XbzxuZD9TLzSLQt0ofof9++tr1iB0Ep8GwvFIHJ81G5E4TwkXzPHovGYlMY2IMyYjeiaLAfFpfJ5m8c7NB7JmYA5DLv8CYWa1ZYuU+HE8821J+kS4cVVTlUg7S8Twl/OUBVEiaODkjoaJZ4rQVJ03B4xTR3gzWSAOZzJW03EJJ46Qr6hWsyIeTtiAOqHvk2CQWtLD/Kx5nlp26A1URKGX1pvz+YOaxWlAL5bghDo5qGKyhxlUsyoE8XBrtdoDcyvnYllUqplEEeWmI0dWj4rO6DzzlO4pL1rQT6VKgzjhVEWTk0/nEN0E6CZGtwC6hdFnAH2G0W2AbmP0OUCfY3QHoDsY3QXoLkb3ALqH0X2A7mP0BUBfYLQF0BZGXwL0JUYPAHqA0VcAfYXRQ4AeYvQ1QF9j9A1A32D0CKBHGD0G6DFG2wBtY7QD0A5GuwDtYvQEoCcY7QG0h9FTgJ5e8xHKzWVAAG8VCh4NNvKhUS5Am0vKQ2DSULSOhwGN59k6m1LU3KTqXpHY88QGqI1RB6AORgcAHWCUApRidAjQIUZHAB1h1AWoi1EGUIbRtwB9i9ExQMcY9QDqYdQHqI/RAKABRqtfqUJDjEYAjTD6DqDvMMoByjEaAzTGqACowGgC0ASjE4BOMHoB0AuMTgE6xegMoDOMXgL08pqBBdNAJnypFWVzQeZ1scw4I7GS2ZUTxPhpntS50kylaxV1s6Ruaup2Sd3W1L2Suqep+yV1X1MPSuqBph6V1CNNPSmpJ5raK6m9/BW5RMTfrWJulni6aquQpXlV3FmKO5q43Knc8u5UgY5dKpZM/qA5aS+dtHWxsxQ7uthdil1N9FbC83B4ohyegOFl0yTTZUkTZ0txpouXS/FSE3uF1tOU00I51ZS4t+zv1cCWP34vvMAfv5q/jssyNjsAjTil41XIJl7kqpchgeL4ZOVVuYvQp2Zx4HMWx6mVBlg0P9uQ5y+PDoV84cHIo2a9+ch6VN+wOBu5wuJZZaVb29OodLiz5QTLWjirN3Or8wq/FU5yP6Gc6USEXJ1+U1W7sCu51I05h9ay+hbmHcLzWFesVe3NMR/y0M7dFp08XBhc48i+OhvTEQtS9czZdC4dUKkvHitWg8E09zKUh265Nqr7AuLJQZhfPUz7aX1jXrUkXOaJ09xjEgzkeZ2KNLNb6WmBIWsW3MqaBZq1rGP/a6sgP/F1YzK9hbGEkHGs9mBBpyKNE/stdYS6yqhCQr5LCkY9r8+G8eFi3H/Ipoq6erHJjMaMBCYLigui1VYjzkKVV3A37FcajrgWaEbPrsUfaYtPZnB5vYG2IHlsjGklaN+ZE6o8Y4fI536Welfdh9mrRc7DWGvOyXHndixTpNr3K6vjqFgcR9q6mSUP2bqpsoVKe27eYAmoECMayaxu1JdHHC6LzAuDam9Zhsj/N0BOQSlXFVDrSd5c3pkbmnQXjheh3+TeLfmHvLa/Fw23qkora6d1U2Ctq7haN0U1FTxRh7GJXJXyiZhVqB2nf6/erF6R6oXOxuNm43HzdaP+5Kfi+vSu8a3xvfHQaBo/G0+MXePQaBuOMTZ+NX4zfl//Y/3P9b/W/87RO2uFzTfGym/9n/8AoArDfw==</latexit>

    <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> find such that s ( x ) <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> Radial basis approximation a queryable function GIVEN f ( x ) centers x1, . . . , xn <latexit 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<latexit 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<latexit sha1_base64="FqyAIE90iFEsMkh76qjqpRo5BVw=">AAAWJHicjZhNb9s2GMfV7q3z3toNOe2izSjQAUFhB8O2Y5s0TZO6adrETpzYMCiZltjorRTl2BH0OXbdLvs0uw077LLPMlKSHVn8J4uBIBT/v4fPQ1IkH8qKPBaLVuufO3c/+PCjjz+592njs8+/+PKr+w++7sVhwm3atUMv5CcWianHAtoVTHj0JOKU+JZHj63zLaUfTymPWRgciXlEhz5xAjZhNhGyajgbtdcH41DE67NRMLrfbD1u5T9TL7TLQtMofwejB2t3pLGd+DQQtkfi+KzdisQwJVww26NZY5DENCL2OXHomSwGxKfxMM2jzsyHsmZsTkIu/wJh5rVVi5T4cTz3LUn6RLhxXVOVSDtLxOSXYcqCKBE0sAtHk8QzRWiqITDHjFNbeHNZIDZnMlbTdgkntpAD1WgMIh5O2Zjaoe+TYJwOpIfsrD1MB1bojVVEoZc221n2sDHgNKAXS3BK7QJUMVmTHGoMagTxcGuNxkNzq+BiWVSqmUQR5aYt51ePis5plntKd5UXLeinUqVBnHCqoinIpxlENwG6idEtgG5h9BlAn2F0G6DbGH0O0OcY3QHoDkZfAPQFRncBuovRPYDuYfQlQF9itAPQDkZfAfQVRvcBuo/R1wB9jdEDgB5g9A1A32D0LUDfYvQQoIcYPQLoEUa7AO1itAfQHkaPAXqM0ROAnmC0D9A+Rk8BenrNSyiPmDEB/KBU8Gwwx4dGhQBtLikPgUlL0ToeBjTO8n02pai5ad29IrHnqQVQC6M2QG2MjgE6xigFKMXoBKATjDoAdTDqAtTFKAMow+g7gL7D6DlAzzHqAdTDqA9QH6MBQAOM1t9ShYYYjQAaYfQ9QN9jlAOUYzQGaIxRAVCB0QSgCUanAJ1i9AKgFxidAXSG0TlA5xi9BOjlNRMLloFM+NJBlK8FmdfFMuOMxEpmV00Q46dFUudKM5Wu1dTNirqpqdsVdVtTdyvqrqbuVdQ9Td2vqPuaelhRDzX1pKKeaGq/ovaLIXKJiL9bxdw88XTVUSFLWV3cWYo7mrg8qdzq6VSDjlwqlkzxoDnpLp10dbG3FHu6eLwUjzXRWwnPw+GJangChpcvk1yXJU2cL8W5Ll4uxUtN7JdaX1NOS+VUU+L+sr9XE1t9+b3wAr/8av3aLsvZ/ALkcErPVyGLeJGrBkMC5fVpUFQVLkKfmuWFz15cp1YaYFF2tiHvXx6dCDnggeNRsymvwevNjQFnjisGPK+sdWt7FlUud5ZcYHkLZ812YTWs8VvhtPATypVORMjV7TdVtQu7ikvdmHNoLatvYd4jvIh1xVrV3hzzAQ+twm3ZyYOFwTWOrKu7MXVYkKpnzmaZdEClvnisWY3Hs8LLRF665d6ovhcQT05CdvUwG6XNjaxuSbjME2eFxyQYy/s6FWlut9LTEkPWLLiVNQs0a1nH/tdWQX7i68ZkdgtjCSHjWJ3Bgs5EGifWO2oL9SmjDgk5lhTMelGfT+Ojxbz/kC8V9enFInMaMxKYLCg/E622GnEWqryCu+Go1nDEtUBzen4tvq5tPrnB5fUG2obksXNMK0F7z+xQ5Rk7RD6P8tS77j7MhxY5D2OtObvA7duxTJHq3K/tjk65OTravpknD/m+qbKFWntu0WAFqBEOjWRW54zkFYfLIvPCoN5bliPy/w2QXVLKVQ3UelI0V3TmhibdheNF6De5dyv+Ia+d72XDnbrSydvp3BRY5yquzk1RzQRP1GVsKnelYiHmFerEGd1vtuufSPVCb+Nxu/W4/ebH5pOfys+n94xvje+NR0bb+Nl4YrwwDoyuYRvvjV+N34zf1/5Y+3Ptr7W/C/TundLmG2Plt/bvf+KExcQ=</latexit> <latexit sha1_base64="FqyAIE90iFEsMkh76qjqpRo5BVw=">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</latexit> GOAL QUERY THE FUNCTION yi = f ( xi) <latexit 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<latexit 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<latexit 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<latexit sha1_base64="DSMIHsDlFYUZwiwOabLZEBLNT+s=">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</latexit> CHOOSE KERNEL (x, x 0 ; ") = exp(" | x x 0|2 ) <latexit sha1_base64="HvFcm2PJ26lSUDpyVkXpnM24lRc=">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</latexit> <latexit sha1_base64="HvFcm2PJ26lSUDpyVkXpnM24lRc=">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</latexit> <latexit sha1_base64="HvFcm2PJ26lSUDpyVkXpnM24lRc=">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</latexit> <latexit 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x y DEFINES BASIS i( x ) =  ( x, xi; " ) <latexit 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<latexit 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<latexit 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<latexit 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COMPUTE COEFFICIENTS Ka = f Kij =  ( xi, xj) , fi = f ( xi) <latexit 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<latexit 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<latexit 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<latexit 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  51. the error is small ks fk <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit>

    <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> <latexit sha1_base64="Ke5uS1R93aIAQ9a5Cjppm3RdEDo=">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</latexit> find such that s ( x ) <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> <latexit sha1_base64="5XvCBZOj0rO8DiDAh35yBu0tPfY=">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</latexit> Radial basis approximation a queryable function GIVEN f ( x ) centers x1, . . . , xn <latexit 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<latexit 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<latexit sha1_base64="FqyAIE90iFEsMkh76qjqpRo5BVw=">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</latexit> <latexit sha1_base64="FqyAIE90iFEsMkh76qjqpRo5BVw=">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</latexit> GOAL QUERY THE FUNCTION yi = f ( xi) <latexit 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<latexit 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<latexit 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<latexit sha1_base64="DSMIHsDlFYUZwiwOabLZEBLNT+s=">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</latexit> CHOOSE KERNEL (x, x 0 ; ") = exp(" | x x 0|2 ) <latexit sha1_base64="HvFcm2PJ26lSUDpyVkXpnM24lRc=">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</latexit> <latexit 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<latexit 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<latexit 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DEFINES BASIS i( x ) =  ( x, xi; " ) <latexit 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<latexit 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<latexit 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<latexit 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x y COMPUTE COEFFICIENTS Ka = f Kij =  ( xi, xj) , fi = f ( xi) <latexit sha1_base64="GjWvcbZWi4edaSsJYRLRf8mjKrw=">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</latexit> <latexit sha1_base64="GjWvcbZWi4edaSsJYRLRf8mjKrw=">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</latexit> <latexit 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<latexit 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PREDICT s ( x ) = X i ai i( x ) <latexit 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<latexit 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<latexit 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  52. Radial basis approximation x y Gaussian process regression x y

  53. Radial basis approximation Gaussian process regression x y x y

    The story of the data and fitted curve is different. But does it matter? YES
  54. Comments on error and convergence GP conditional variance is NOT

    error (except possibly under some very specific conditions) . RBF error estimates are asymptotic in the fill distance. Both approaches make practically unverifiable assumptions about the origin of the data generating function/process. As a caricature: statisticians try to reduce the error by finding a better model (e.g., solve the fitting problem better) mathematicians try to reduce the error with more queries (i.e., sample into asymptopia)
  55. Regression Approximation x y x y Which one is a

    computer simulation? x y x y
  56. Sacks et al. (1989) What is error in a computer

    simulation? Kennedy and O’Hagan (2001)
  57. What is error in a computer simulation? Oberkampf et al.

    (2002) von Neumann and Goldstine Bulletin of the AMS (1947) [h/t Joe Grcar]
  58. “This analysis of the sources of errors should be objective

    and strict inasmuch as completeness is concerned, but when it comes to the defining, classifying, and separating of the sources, a certain subjectiveness and arbitrariness is unavoidable. With these reservations, the following enumeration and classification of sources of errors seems to be adequate and reasonable.” Mathematical model Observations and parameters Finitistic approximations Round-off The von Neumann and Goldstine Catechism
  59. “This analysis of the sources of errors should be objective

    and strict inasmuch as completeness is concerned, but when it comes to the defining, classifying, and separating of the sources, a certain subjectiveness and arbitrariness is unavoidable. With these reservations, the following enumeration and classification of sources of errors seems to be adequate and reasonable.” Mathematical model Observations and parameters Finitistic approximations Round-off The von Neumann and Goldstine Catechism NOTES How well math model approximates reality Model-form error
  60. “This analysis of the sources of errors should be objective

    and strict inasmuch as completeness is concerned, but when it comes to the defining, classifying, and separating of the sources, a certain subjectiveness and arbitrariness is unavoidable. With these reservations, the following enumeration and classification of sources of errors seems to be adequate and reasonable.” Mathematical model Observations and parameters Finitistic approximations Round-off The von Neumann and Goldstine Catechism NOTES Forward and inverse UQ Most of the UQ methods literature
  61. “This analysis of the sources of errors should be objective

    and strict inasmuch as completeness is concerned, but when it comes to the defining, classifying, and separating of the sources, a certain subjectiveness and arbitrariness is unavoidable. With these reservations, the following enumeration and classification of sources of errors seems to be adequate and reasonable.” Mathematical model Observations and parameters Finitistic approximations Round-off The von Neumann and Goldstine Catechism NOTES Asymptotics from classical numerical analysis Deterministic numerical noise “Computational noise in deterministic simulations is as ill-defined a concept as can be found in scientific computing.” Moré and Wild (2011)
  62. Computer models are deterministic. In my opinion, approximation tools are

    better suited. But computational noise is really annoying, if you take it seriously. LOTS of fundamental research opportunities for applying statistical methods to noise-less data--- i.e., the approximation setting. What does Bayes have to do with it? Summary thoughts
  63. Everyone, civilized conversation and argumentation!!! Statisticians, include numerical experiments that

    demonstrate asymptotic convergence of testing error. Numerical analysts, convergence analysis of statistical standard error and bootstrap standard error in the context of constructive approximation. Write three review papers: Regression for numerical analysts Approximation for statisticians Reconciling perspective with authors from both communities Practical advice
  64. PAUL CONSTANTINE Assistant Professor University of Colorado Boulder activesubspaces.org! @DrPaulynomial!

    QUESTIONS? Active Subspaces SIAM (2015) Why should we care? What do you do in practice?