class_docstr: Represents datasets we use for expriments
docstr: Generates a synthetic dataset for logistic regression.
  
  n = number of samples d = dimension Features are unit vectors (by default
  uniformly random). Labels are sampled from logistic distribution, so w is
  the "true" solution.
docstr_tok: ["Generates","a","synthetic","dataset","for","logistic","regression",".","n","=","number","of","samples","d","=","dimension","Features","are","unit","vectors","(","by","default","uniformly","random",")",".","Labels","are","sampled","from","logistic","distribution",",","so","w","is","the","``","true","''","solution","."]
code: def synthetic_dataset(self, num_samples=10000, dim=100):
      """Generates a synthetic dataset for logistic regression.
  
      n = number of samples d = dimension Features are unit vectors (by default
      uniformly random). Labels are sampled from logistic distribution, so w is
      the "true" solution.
      """
      mean = np.zeros(dim)
      cov = np.eye(dim)
      inputs_vec_un = np.random.multivariate_normal(
          mean, cov, num_samples
      )
      nrm = np.linalg.norm(inputs_vec_un, axis=1)
      inputs_vec = inputs_vec_un * 1 / nrm[:, None]
      w_star = np.ones(dim)
      w_star[0] = 1
      inner_prod = np.dot(inputs_vec, w_star)
      params = np.exp(inner_prod) / (1 + np.exp(inner_prod))
      labels = 2 * np.random.binomial(1, params) - 1
      dataset = inputs_vec, labels
      w_opt = self.find_optimal_classifier(dataset, bias=False)
      return inputs_vec, labels, w_opt
  
imports: import os
  import ssl
  import tarfile
  import urllib.request
  from my_logistic_regression import MyLogisticRegression
  import numpy
  import requests
  from sklearn import preprocessing
  import sklearn.datasets
  from sklearn.linear_model import LogisticRegression
  import torch
  from torchvision import datasets, transforms
label_desc: Use image node_id 6 for calling the Mydatasets obj's underlying member method code with example usage: obj.synthetic_dataset(num_samples, dim) and returns: inputs_vec,  labels,  w_opt