CS-GY 6923: Machine Learning
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  • Introduction
  • What is Machine Learning?
  • Types of Machine Learning
    • Supervised Learning
      • Notations
      • Probabilistic Modeling
        • Naive Bayes Classifier
      • Linear Regression
      • Nearest Neighbor
      • Evaluating a Classifier
      • Parametric Estimation
        • Bayesian Approach to Parameter Estimation
        • Parametric Estimation for Simple Linear Regression
        • Parametric Estimation for Multivariate Linear Regression
        • Parametric Estimation for Simple Polynomial Regression
        • Parametric Estimation for Multivariate Polynomial Regression
      • Bias and Variance of an Estimator
      • Bias and Variance of a Regression Algorithm
        • Model Selection
      • Logistic Regression
      • Decision Trees
        • Using Decision Trees for Regression
        • Bias and Variance
      • Dimensionality Reduction
      • Neural Networks
        • Training a Neuron
        • MLP
          • Regression with Multiple Outputs
          • Advice/Tricks and Issues to Train a Neural Network
        • Deep Learning
      • Support Vector Machines
      • Ensemble Learning
    • Unsupervised Learning
      • K-Means Clustering
      • Probabilistic Clustering
    • Reinforcement Learning
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  1. Types of Machine Learning
  2. Supervised Learning
  3. Neural Networks
  4. MLP

Regression with Multiple Outputs

The aim here is to predict multiple values, instead of just a single value. This is analogous to multi-label classification where we attempt to predict multiple classses at once.

Reasons to do so:

  • less training time

  • less number of weights, therefore, less prone to overfitting

  • possible relation between values being predicted can be learned

The Error Function is as follows:

E=∑i=1k∑t=1N(rit−yit)2E = \sum_{i=1}^k \sum_{t=1}^N (r_i^t-y_i^t)^2E=∑i=1k​∑t=1N​(rit​−yit​)2

i.e. the mean squared error. (k is the number of values to be predicted)

  • can use stochastic gradient descent

  • can use mini-batches in the gradient descent

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Last updated 5 years ago

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