# 2: Training Deep NNs (cont.); Introduction to Keras/Tensorflow; Application to Tabular Data Source: https://www.youtube.com/watch?v=3Lr8nVUDCpk Recap page: https://rapidrecap.app/video/3Lr8nVUDCpk Generated: 2026-01-07T16:00:59.126+00:00 --- ## Quick Overview Training a deep neural network involves designing the architecture, selecting a loss function appropriate for the output type (like binary cross-entropy for classification), and minimizing that loss using the gradient descent optimization algorithm, which generalizes the 19th-century method for high-dimensional parameter spaces like those in large models such as GPT-4. **Key Points:** - The rule of thumb for designing a network is to start with the simplest network and only increase complexity if performance is insufficient. - The case study involves predicting heart disease diagnosis within one year using structured patient data from the Cleveland Clinic, featuring demographic and biomarker information. - For the binary classification problem (heart disease yes/no), the network uses one hidden layer with 16 ReLU neurons and a sigmoid activation in the output layer to emit a probability. - The input layer size was determined to be 29 features after one-hot-encoding some of the initial 13 input variables. - The Mean Squared Error (MSE) is the loss function for regression, but for binary classification with sigmoid output, the Binary Cross Entropy loss function, expressed as minus log probability or minus log(1-probability), is utilized. - Training involves minimizing the loss function by finding optimal weights and biases using Gradient Descent, an algorithm invented by Cauchy in 1847, implemented by iteratively updating parameters using the gradient (vector of partial derivatives) and a learning rate (alpha). - In high-dimensional spaces (like models with billions of parameters), gradient descent stops near local minima or saddle points, which is empirically sufficient and avoids the risk of overfitting associated with finding a global minimum. **Context:** The lecture continues the discussion on training deep neural networks, focusing on the practical steps and conceptual foundations required, such as optimization and loss functions. The discussion centers around a case study using structured data from the Cleveland Clinic to predict future heart disease diagnosis for patients presenting with other issues, setting up a classic binary classification problem to demonstrate the process using Keras/TensorFlow implementation. ## Detailed Analysis The lecture establishes that network design requires choosing the number of hidden layers, neurons per layer, and activation functions, recommending ReLU for hidden layers as a default based on empirical evidence. For the heart disease prediction case study, a network with one hidden layer of 16 ReLU neurons and a sigmoid output was chosen after empirical testing showed better results than other neuron counts, leading to 29 input features due to one-hot encoding categorical variables. The parameter count for this specific architecture was calculated to be 497, illustrating the rapid parameter explosion in fully connected layers. The speaker then translates this design into Keras code using `keras.Input`, `keras.layers.Dense` (with ReLU activation), and a final `Dense` layer with sigmoid activation, formally defining the model using `keras.Model`. Training is explained as finding coefficients (weights and biases) that minimize the discrepancy between predictions and actual values, quantified by a loss function. For the binary classification output (0 or 1), the Binary Cross Entropy loss function is derived, mathematically combining the need for high loss when predicting near zero for a true positive (y=1) and high loss when predicting near one for a true negative (y=0) using the negative logarithm of the relevant probability term. Minimizing this loss is achieved via Gradient Descent, generalized from its 1847 origin to high dimensions by calculating the gradient (the vector of partial derivatives) across all parameters and iteratively updating them using the formula: new_w = old_w - alpha * gradient, where alpha is the learning rate; this process is deemed effective even if it only finds local minima or saddle points, especially in complex models like GPT-4. ### Neural Network Design Principles - Start simple and only increase complexity if needed - ReLU is the default hidden layer activation - Design choices like layer count and neuron count require trial and error. ### Case Study Setup - Predicting heart disease diagnosis within one year using structured patient data from Cleveland Clinic - Input variables included demographics and biomarkers - The task is framed as a binary classification problem. ### Architecture Specification - Chosen architecture includes one hidden layer with 16 ReLU neurons - Output layer uses sigmoid activation for probability emission - Input feature count is 29 after one-hot-encoding categorical variables. ### Keras Model Construction - Model is defined sequentially using `keras.Input(shape=29)` - Hidden layer is defined as `keras.layers.Dense(16, activation='relu')` - The final layer is a `Dense` layer with one unit and sigmoid activation, connected using variable names to map flow. ### Loss Function Derivation - For binary classification, Binary Cross Entropy loss is used, derived from $-\log(p)$ when $y=1$ and $-\log(1-p)$ when $y=0$, combined into a single expression using $y_i$. - Loss quantifies the 'badness' of the model's predictions. ### Optimization via Gradient Descent - Training minimizes the loss function using Gradient Descent, an 1847 algorithm - The update rule is $w_{new} = w_{old} - \alpha \cdot \nabla g(w)$ - In high dimensions, stopping at local minima or saddle points is sufficient and avoids overfitting.