deep learning in medicine

Task T:

  • Classification: output is a category
  • Regression: continuous vs discreet
  • anomaly detection: EEG data
  • synthesis and sampling
  • density estimation or probability mass function estimation
    • ie clusters of distribution

Performance Measure, P:

  • Accuracy of predicted labels compared to true labels
  • mean squared error between target and predictions
  • likelihood: probability of predicting the true outcome label for samples
    • classification
    • function of the model parameters
    • conditional probability
    • i.i.d. = identically and independently drawn

Machine learning formulation:

  • input: X
  • output: Y
  • task: fθ(x)
  • evaluation: loss

Supervised Learning- Classification

  • input X: continuous or categorical vector or Matrix or Tensor
  • output Y: categorical label
  • task fθ(x): some function f that computes probability of the each for each sample
  • evaluation loss

Supervised Learning- Regression

  • input X: continuous or categorical vector or Matrix or Tensor
  • output Y: continuous target
  • task fθ(x): some function f that computes target for each sample
  • evaluation loss: mean squared error loss, or adversarial loss, etc

Supervised Learning- Structured Output

  • input X: continuous or categorical vector or Matrix or Tensor
  • output Y: continuous or categorical vector or Matrix or Tensor
  • task fθ(x): some function f that computes  a vector/matrix/tensor for each sample
  • evaluation loss: combination

Unsupervised Learning- Density Estimation

  • input X: continuous or categorical vector or Matrix or Tensor
  • output Y: P(X)
  • task fθ(x):
  • evaluation loss: log likelihood of observing Xs are they are

Unsupervised Learning- Denoising

  • input X (noisy): continuous or categorical vector or Matrix or Tensor
  • output X: denoised continuous or categorical vector or Matrix or Tensor
  • task fθ(x): some function that returns an output identical in size but with nice constraints
  • evaluation loss

Gradient descent: used to find the local minimum

Solution to under/overfitting:

  • randomly sample and set aside a test set; the rest of the data becomes the training set
  • optimize the loss function on the training set only
  • have 3 sets: training set, validation set, and test set