clojure - 用BFGS最小化算法努力解决Clojure中带有Loganter的Logistic回归问题

我正在尝试使用Incanter data analysis库在Clojure中实现一个简单的逻辑回归示例。我已经成功编写了Sigmoid和Cost函数，但是Incanter的BFGS最小化函数似乎给我带来了很多麻烦。

(ns ml-clj.logistic
  (:require [incanter.core :refer :all]
            [incanter.optimize :refer :all]))


(defn sigmoid
  "compute the inverse logit function, large positive numbers should be
close to 1, large negative numbers near 0,
z can be a scalar, vector or matrix.
sanity check: (sigmoid 0) should always evaluate to 0.5"
  [z]
  (div 1 (plus 1 (exp (minus z)))))

(defn cost-func
  "computes the cost function (J) that will be minimized
   inputs:params theta X matrix and Y vector"
  [X y]
  (let
      [m (nrow X)
       init-vals (matrix (take (ncol X) (repeat 0)))
       z (mmult X init-vals)
       h (sigmoid z)
       f-half (mult (matrix (map - y)) (log (sigmoid (mmult X init-vals))))
       s-half (mult (minus 1 y) (log (minus 1 (sigmoid (mmult X init-vals)))))
       sub-tmp (minus f-half s-half)
       J (mmult (/ 1 m) (reduce + sub-tmp))]
    J))

当我尝试(minimize (cost-func X y) (matrix [0 0]))给minimize一个函数并启动参数时，REPL会引发错误。

ArityException Wrong number of args (2) passed to: optimize$minimize  clojure.lang.AFn.throwArity (AFn.java:437)

我对最小化功能到底期望什么感到非常困惑。

作为参考，我用python重写了所有代码，并且所有代码都使用相同的最小化算法按预期运行。

import numpy as np
import scipy as sp
data = np.loadtxt('testSet.txt', delimiter='\t')

X = data[:,0:2]
y = data[:, 2]


def sigmoid(X):
    return 1.0 / (1.0 + np.e**(-1.0 * X))

def compute_cost(theta, X, y):
    m = y.shape[0]
    h = sigmoid(X.dot(theta.T))
    J = y.T.dot(np.log(h)) + (1.0 - y.T).dot(np.log(1.0 - h))
    cost = (-1.0 / m) * J.sum()
    return cost

def fit_logistic(X,y):
    initial_thetas = np.zeros((len(X[0]), 1))
    myargs = (X, y)
    theta = sp.optimize.fmin_bfgs(compute_cost, x0=initial_thetas,
                                     args=myargs)
    return theta

输出

Current function value: 0.594902
         Iterations: 6
         Function evaluations: 36
         Gradient evaluations: 9
array([ 0.08108673, -0.12334958])

我不明白为什么Python代码可以成功运行，但是我的Clojure实现失败。有什么建议么？

更新资料

重新读取minimize的文档字符串，我一直在尝试计算cost-func的派生类，这将引发新的错误。

(def grad (gradient cost-func (matrix [0 0])))
(minimize cost-func (matrix [0 0]) (grad (matrix [0 0]) X))
ExceptionInfo throw+: {:exception "Matrices of different sizes cannot be differenced.", :asize [2 1], :bsize [1 2]}  clatrix.core/- (core.clj:950)

使用trans将1xn col矩阵转换为nx1行矩阵只会产生相同的错误，但具有相反的错误。

:asize [1 2], :bsize [2 1]}

我在这里很迷路。

最佳答案

关于您的实现，我什么也没说，但是incanter.optimize/minimize期望（至少）三个参数，而您只给了两个参数：

Arguments:
  f -- Objective function. Takes a collection of values and returns a scalar
       of the value of the function.
  start -- Collection of initial guesses for the minimum
  f-prime -- partial derivative of the objective function. Takes
             a collection of values and returns a collection of partial
             derivatives with respect to each variable. If this is not
             provided it will be estimated using gradient-fn.

不幸的是，我无法在这里直接告诉您要提供什么（f-prime？），但也许有人可以提供。顺便说一句，我认为ArityException Wrong number of args (2) passed to [...]实际上在这里很有帮助。

编辑：实际上，我认为上面的文档字符串不正确，因为源代码未使用gradient-fn来估计f-prime。也许您可以使用incanter.optimize/gradient生成自己的？