🚀

💡 Pro tip: This is one of those techniques that will make you look like a data science wizard! Generative Data Augmentation (GDA) - Made Simple!

Generative Data Augmentation is a technique that uses generative models to create synthetic data for training machine learning models. This way helps to increase dataset size and diversity, potentially improving model performance and generalization.

Let’s make this super clear! Here’s how we can tackle this:

import numpy as np
from sklearn.datasets import make_moons
from sklearn.model_selection import train_test_split
import matplotlib.pyplot as plt

# Generate original dataset
X, y = make_moons(n_samples=1000, noise=0.1, random_state=42)

# Split the data
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Simple GDA: Add Gaussian noise to existing samples
def augment_data(X, y, n_augmented=500, noise_scale=0.1):
    indices = np.random.choice(len(X), n_augmented, replace=True)
    X_augmented = X[indices] + np.random.normal(0, noise_scale, size=(n_augmented, 2))
    y_augmented = y[indices]
    return np.vstack((X, X_augmented)), np.hstack((y, y_augmented))

# Augment the training data
X_train_aug, y_train_aug = augment_data(X_train, y_train)

# Visualize original and augmented data
plt.figure(figsize=(12, 5))
plt.subplot(121)
plt.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap='viridis')
plt.title("Original Data")
plt.subplot(122)
plt.scatter(X_train_aug[:, 0], X_train_aug[:, 1], c=y_train_aug, cmap='viridis')
plt.title("Augmented Data")
plt.tight_layout()
plt.show()

🚀

🎉 You’re doing great! This concept might seem tricky at first, but you’ve got this! ELBO Loss (Evidence Lower BOund) - Made Simple!

ELBO is a key concept in variational inference, used to approximate the marginal likelihood of observed data. It provides a lower bound on the evidence (log likelihood) and is used as an optimization objective in variational autoencoders (VAEs) and other probabilistic models.

Don’t worry, this is easier than it looks! Here’s how we can tackle this:

import tensorflow as tf
import tensorflow_probability as tfp

class VAE(tf.keras.Model):
    def __init__(self, latent_dim):
        super(VAE, self).__init__()
        self.latent_dim = latent_dim
        self.encoder = tf.keras.Sequential([
            tf.keras.layers.InputLayer(input_shape=(28, 28, 1)),
            tf.keras.layers.Conv2D(32, 3, activation='relu'),
            tf.keras.layers.Flatten(),
            tf.keras.layers.Dense(latent_dim * 2)
        ])
        self.decoder = tf.keras.Sequential([
            tf.keras.layers.InputLayer(input_shape=(latent_dim,)),
            tf.keras.layers.Dense(7*7*32, activation='relu'),
            tf.keras.layers.Reshape((7, 7, 32)),
            tf.keras.layers.Conv2DTranspose(1, 3, strides=2, padding='same',
                                            activation='sigmoid')
        ])

    def encode(self, x):
        mean, logvar = tf.split(self.encoder(x), num_or_size_splits=2, axis=1)
        return mean, logvar

    def reparameterize(self, mean, logvar):
        eps = tf.random.normal(shape=mean.shape)
        return eps * tf.exp(logvar * .5) + mean

    def decode(self, z):
        return self.decoder(z)

    def compute_loss(self, x):
        mean, logvar = self.encode(x)
        z = self.reparameterize(mean, logvar)
        x_logit = self.decode(z)
        
        # Reconstruction loss
        cross_ent = tf.nn.sigmoid_cross_entropy_with_logits(logits=x_logit, labels=x)
        logpx_z = -tf.reduce_sum(cross_ent, axis=[1, 2, 3])
        
        # KL divergence
        logpz = tfp.distributions.Normal(0., 1.).log_prob(z)
        logqz_x = tfp.distributions.Normal(mean, tf.exp(logvar)).log_prob(z)
        
        # ELBO
        elbo = tf.reduce_mean(logpx_z + tf.reduce_sum(logpz - logqz_x, axis=1))
        
        return -elbo  # We minimize the negative ELBO

# Usage
vae = VAE(latent_dim=2)
optimizer = tf.keras.optimizers.Adam(1e-4)

@tf.function
def train_step(x):
    with tf.GradientTape() as tape:
        loss = vae.compute_loss(x)
    gradients = tape.gradient(loss, vae.trainable_variables)
    optimizer.apply_gradients(zip(gradients, vae.trainable_variables))
    return loss

# Train the VAE (assuming 'train_dataset' is defined)
for epoch in range(100):
    for batch in train_dataset:
        loss = train_step(batch)
    print(f'Epoch {epoch + 1}, Loss: {loss.numpy()}')

🚀

✨ Cool fact: Many professional data scientists use this exact approach in their daily work! Heuristic-based Losses - Made Simple!

Heuristic-based losses are custom loss functions designed to incorporate domain knowledge or specific objectives into the training process. These losses can guide the model towards desired behaviors or properties that are not captured by standard loss functions.

Let’s break this down together! Here’s how we can tackle this:

import tensorflow as tf

def focal_loss(y_true, y_pred, alpha=0.25, gamma=2.0):
    """
    Focal Loss: A loss function that addresses class imbalance by
    down-weighting easy examples and focusing on hard ones.
    """
    epsilon = 1e-7
    y_pred = tf.clip_by_value(y_pred, epsilon, 1. - epsilon)
    
    # Calculate cross entropy
    cross_entropy = -y_true * tf.math.log(y_pred)
    
    # Calculate focal loss
    loss = alpha * tf.pow(1. - y_pred, gamma) * cross_entropy
    
    return tf.reduce_mean(loss)

def triplet_loss(y_true, y_pred, margin=1.0):
    """
    Triplet Loss: Used in metric learning to minimize distance between
    similar samples and maximize distance between dissimilar ones.
    """
    anchor, positive, negative = tf.unstack(y_pred, axis=1)
    
    pos_dist = tf.reduce_sum(tf.square(anchor - positive), axis=1)
    neg_dist = tf.reduce_sum(tf.square(anchor - negative), axis=1)
    
    loss = tf.maximum(pos_dist - neg_dist + margin, 0.0)
    return tf.reduce_mean(loss)

# Example usage
model = tf.keras.Sequential([
    tf.keras.layers.Dense(64, activation='relu'),
    tf.keras.layers.Dense(1, activation='sigmoid')
])

model.compile(optimizer='adam', loss=focal_loss)

# For triplet loss, the model architecture and data preparation would be different
# Here's a simplified example:
triplet_model = tf.keras.Sequential([
    tf.keras.layers.Dense(64, activation='relu'),
    tf.keras.layers.Dense(32)
])

triplet_model.compile(optimizer='adam', loss=triplet_loss)

# Training would involve creating triplets of (anchor, positive, negative) samples

🚀

🔥 Level up: Once you master this, you’ll be solving problems like a pro! Bayes’ Theorem - Made Simple!

Bayes’ Theorem is a fundamental concept in probability theory and statistics. It describes the probability of an event based on prior knowledge of conditions that might be related to the event. This theorem is widely used in machine learning for tasks such as classification and inference.

Here’s a handy trick you’ll love! Here’s how we can tackle this:

import numpy as np
import matplotlib.pyplot as plt

def bayes_theorem(prior, likelihood, evidence):
    """
    Calculate the posterior probability using Bayes' Theorem.
    
    P(A|B) = (P(B|A) * P(A)) / P(B)
    
    Where:
    P(A|B) is the posterior probability
    P(B|A) is the likelihood
    P(A) is the prior probability
    P(B) is the evidence
    """
    return (likelihood * prior) / evidence

# Example: Medical diagnosis
# Prior probability of having the disease
prior_disease = 0.01

# Likelihood of positive test given disease
sensitivity = 0.95

# Probability of positive test (evidence)
false_positive_rate = 0.10
evidence = sensitivity * prior_disease + false_positive_rate * (1 - prior_disease)

# Calculate posterior probability
posterior = bayes_theorem(prior_disease, sensitivity, evidence)

print(f"Probability of having the disease given a positive test: {posterior:.4f}")

# Visualize how posterior changes with different prior probabilities
priors = np.linspace(0, 1, 100)
posteriors = bayes_theorem(priors, sensitivity, evidence)

plt.figure(figsize=(10, 6))
plt.plot(priors, posteriors)
plt.title("Posterior Probability vs Prior Probability")
plt.xlabel("Prior Probability of Disease")
plt.ylabel("Posterior Probability of Disease")
plt.grid(True)
plt.show()

🚀 Reparameterization Trick - Made Simple!

The reparameterization trick is a technique used in variational inference and generative models to allow backpropagation through random variables. It’s particularly useful in training Variational Autoencoders (VAEs) and other stochastic neural networks.

Don’t worry, this is easier than it looks! Here’s how we can tackle this:

import tensorflow as tf
import tensorflow_probability as tfp
import matplotlib.pyplot as plt

# Define a simple VAE model
class SimpleVAE(tf.keras.Model):
    def __init__(self, latent_dim):
        super(SimpleVAE, self).__init__()
        self.latent_dim = latent_dim
        self.encoder = tf.keras.Sequential([
            tf.keras.layers.Dense(64, activation='relu'),
            tf.keras.layers.Dense(latent_dim * 2)
        ])
        self.decoder = tf.keras.Sequential([
            tf.keras.layers.Dense(64, activation='relu'),
            tf.keras.layers.Dense(1)
        ])
    
    def encode(self, x):
        mean, logvar = tf.split(self.encoder(x), num_or_size_splits=2, axis=1)
        return mean, logvar
    
    def reparameterize(self, mean, logvar):
        eps = tf.random.normal(shape=mean.shape)
        return eps * tf.exp(logvar * .5) + mean
    
    def decode(self, z):
        return self.decoder(z)

# Create and train the model
vae = SimpleVAE(latent_dim=2)
optimizer = tf.keras.optimizers.Adam(1e-3)

@tf.function
def train_step(x):
    with tf.GradientTape() as tape:
        mean, logvar = vae.encode(x)
        z = vae.reparameterize(mean, logvar)
        x_logit = vae.decode(z)
        
        # Compute loss
        reconstruction_loss = tf.reduce_mean(tf.square(x - x_logit))
        kl_loss = -0.5 * tf.reduce_mean(1 + logvar - tf.square(mean) - tf.exp(logvar))
        total_loss = reconstruction_loss + kl_loss
    
    gradients = tape.gradient(total_loss, vae.trainable_variables)
    optimizer.apply_gradients(zip(gradients, vae.trainable_variables))
    return total_loss

# Generate some dummy data
x_train = tf.random.normal((1000, 1))

# Train the model
for epoch in range(100):
    loss = train_step(x_train)
    if epoch % 10 == 0:
        print(f"Epoch {epoch}, Loss: {loss.numpy():.4f}")

# Visualize the learned latent space
z = tf.random.normal((1000, 2))
generated = vae.decode(z)

plt.figure(figsize=(10, 6))
plt.scatter(z[:, 0], z[:, 1], c=generated[:, 0], cmap='viridis')
plt.colorbar(label='Generated Value')
plt.title('Latent Space Visualization')
plt.xlabel('z[0]')
plt.ylabel('z[1]')
plt.show()

🚀 Real-life Example: Image Classification with Data Augmentation - Made Simple!

Data augmentation is widely used in computer vision tasks to improve model performance and generalization. Let’s implement a simple image classification model with data augmentation using the CIFAR-10 dataset.

Don’t worry, this is easier than it looks! Here’s how we can tackle this:

import tensorflow as tf
from tensorflow.keras import layers, models
from tensorflow.keras.datasets import cifar10

# Load and preprocess the CIFAR-10 dataset
(train_images, train_labels), (test_images, test_labels) = cifar10.load_data()
train_images = train_images.astype('float32') / 255
test_images = test_images.astype('float32') / 255

# Define data augmentation
data_augmentation = tf.keras.Sequential([
    layers.RandomFlip("horizontal"),
    layers.RandomRotation(0.1),
    layers.RandomZoom(0.1),
])

# Create the model
model = models.Sequential([
    data_augmentation,
    layers.Conv2D(32, (3, 3), activation='relu', input_shape=(32, 32, 3)),
    layers.MaxPooling2D((2, 2)),
    layers.Conv2D(64, (3, 3), activation='relu'),
    layers.MaxPooling2D((2, 2)),
    layers.Conv2D(64, (3, 3), activation='relu'),
    layers.Flatten(),
    layers.Dense(64, activation='relu'),
    layers.Dense(10)
])

# Compile the model
model.compile(optimizer='adam',
              loss=tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True),
              metrics=['accuracy'])

# Train the model
history = model.fit(train_images, train_labels, epochs=10, 
                    validation_data=(test_images, test_labels))

# Evaluate the model
test_loss, test_acc = model.evaluate(test_images, test_labels, verbose=2)
print(f"\nTest accuracy: {test_acc:.2f}")

# Plot training history
import matplotlib.pyplot as plt

plt.figure(figsize=(12, 4))
plt.subplot(1, 2, 1)
plt.plot(history.history['accuracy'], label='Training Accuracy')
plt.plot(history.history['val_accuracy'], label='Validation Accuracy')
plt.title('Model Accuracy')
plt.xlabel('Epoch')
plt.ylabel('Accuracy')
plt.legend()

plt.subplot(1, 2, 2)
plt.plot(history.history['loss'], label='Training Loss')
plt.plot(history.history['val_loss'], label='Validation Loss')
plt.title('Model Loss')
plt.xlabel('Epoch')
plt.ylabel('Loss')
plt.legend()

plt.tight_layout()
plt.show()

🚀 Real-life Example: Bayesian A/B Testing - Made Simple!

Bayesian A/B testing applies Bayes’ theorem to compare two versions of a product or marketing strategy. It provides a more nuanced understanding of results compared to traditional frequentist methods.

Here’s a handy trick you’ll love! Here’s how we can tackle this:

import numpy as np
import matplotlib.pyplot as plt
from scipy import stats

def bayesian_ab_test(clicks_a, impressions_a, clicks_b, impressions_b, samples=100000):
    # Prior distribution (Beta distribution with alpha=1, beta=1)
    prior_a = stats.beta(1, 1)
    prior_b = stats.beta(1, 1)
    
    # Posterior distributions
    posterior_a = stats.beta(prior_a.args[0] + clicks_a, 
                             prior_a.args[1] + impressions_a - clicks_a)
    posterior_b = stats.beta(prior_b.args[0] + clicks_b, 
                             prior_b.args[1] + impressions_b - clicks_b)
    
    # Sample from posterior distributions
    samples_a = posterior_a.rvs(samples)
    samples_b = posterior_b.rvs(samples)
    
    # Calculate probability that B is better than A
    prob_b_better = (samples_b > samples_a).mean()
    
    return samples_a, samples_b, prob_b_better

# Example usage
clicks_a, impressions_a = 200, 1000
clicks_b, impressions_b = 220, 1000

samples_a, samples_b, prob_b_better = bayesian_ab_test(clicks_a, impressions_a, clicks_b, impressions_b)

plt.figure(figsize=(10, 6))
plt.hist(samples_a, bins=50, alpha=0.5, label='A')
plt.hist(samples_b, bins=50, alpha=0.5, label='B')
plt.title('Posterior Distributions of Conversion Rates')
plt.xlabel('Conversion Rate')
plt.ylabel('Frequency')
plt.legend()
plt.show()

print(f"Probability that B is better than A: {prob_b_better:.2f}")

🚀 Generative Models and VAEs - Made Simple!

Variational Autoencoders (VAEs) are powerful generative models that combine ideas from deep learning and probabilistic graphical models. They learn to encode data into a latent space and generate new samples from this space.

Here’s where it gets exciting! Here’s how we can tackle this:

import tensorflow as tf
from tensorflow import keras

class VAE(keras.Model):
    def __init__(self, latent_dim):
        super(VAE, self).__init__()
        self.latent_dim = latent_dim
        self.encoder = self.build_encoder()
        self.decoder = self.build_decoder()

    def build_encoder(self):
        inputs = keras.Input(shape=(28, 28, 1))
        x = keras.layers.Conv2D(32, 3, activation="relu", strides=2, padding="same")(inputs)
        x = keras.layers.Conv2D(64, 3, activation="relu", strides=2, padding="same")(x)
        x = keras.layers.Flatten()(x)
        x = keras.layers.Dense(16, activation="relu")(x)
        z_mean = keras.layers.Dense(self.latent_dim, name="z_mean")(x)
        z_log_var = keras.layers.Dense(self.latent_dim, name="z_log_var")(x)
        z = Sampling()([z_mean, z_log_var])
        return keras.Model(inputs, [z_mean, z_log_var, z], name="encoder")

    def build_decoder(self):
        latent_inputs = keras.Input(shape=(self.latent_dim,))
        x = keras.layers.Dense(7 * 7 * 64, activation="relu")(latent_inputs)
        x = keras.layers.Reshape((7, 7, 64))(x)
        x = keras.layers.Conv2DTranspose(64, 3, activation="relu", strides=2, padding="same")(x)
        x = keras.layers.Conv2DTranspose(32, 3, activation="relu", strides=2, padding="same")(x)
        outputs = keras.layers.Conv2DTranspose(1, 3, activation="sigmoid", padding="same")(x)
        return keras.Model(latent_inputs, outputs, name="decoder")

    def call(self, inputs):
        z_mean, z_log_var, z = self.encoder(inputs)
        reconstruction = self.decoder(z)
        kl_loss = -0.5 * tf.reduce_mean(z_log_var - tf.square(z_mean) - tf.exp(z_log_var) + 1)
        self.add_loss(kl_loss)
        return reconstruction

class Sampling(keras.layers.Layer):
    def call(self, inputs):
        z_mean, z_log_var = inputs
        batch = tf.shape(z_mean)[0]
        dim = tf.shape(z_mean)[1]
        epsilon = tf.keras.backend.random_normal(shape=(batch, dim))
        return z_mean + tf.exp(0.5 * z_log_var) * epsilon

# Usage example (assuming MNIST dataset is loaded)
vae = VAE(latent_dim=2)
vae.compile(optimizer=keras.optimizers.Adam())
vae.fit(x_train, x_train, epochs=10, batch_size=128)

🚀 Heuristic-based Losses in Natural Language Processing - Made Simple!

In NLP, heuristic-based losses can be used to incorporate linguistic knowledge or task-specific objectives into model training. Here’s an example of a custom loss for machine translation that encourages the model to maintain similar sentence lengths between source and target.

This next part is really neat! Here’s how we can tackle this:

import tensorflow as tf

def length_penalty_loss(y_true, y_pred, alpha=0.1):
    """
    Custom loss that penalizes large differences in sentence length
    between source and target.
    """
    # Assuming y_true and y_pred are sequences of token IDs
    true_length = tf.reduce_sum(tf.cast(tf.not_equal(y_true, 0), tf.float32), axis=-1)
    pred_length = tf.reduce_sum(tf.cast(tf.not_equal(y_pred, 0), tf.float32), axis=-1)
    
    length_diff = tf.abs(true_length - pred_length)
    length_penalty = alpha * tf.square(length_diff)
    
    # Combine with standard cross-entropy loss
    ce_loss = tf.keras.losses.sparse_categorical_crossentropy(y_true, y_pred, from_logits=True)
    total_loss = ce_loss + length_penalty
    
    return total_loss

# Example usage in a translation model
class TranslationModel(tf.keras.Model):
    def __init__(self, vocab_size, embedding_dim, units):
        super(TranslationModel, self).__init__()
        self.embedding = tf.keras.layers.Embedding(vocab_size, embedding_dim)
        self.lstm = tf.keras.layers.LSTM(units, return_sequences=True)
        self.dense = tf.keras.layers.Dense(vocab_size)

    def call(self, inputs):
        x = self.embedding(inputs)
        x = self.lstm(x)
        return self.dense(x)

# Instantiate and compile the model
model = TranslationModel(vocab_size=10000, embedding_dim=256, units=512)
model.compile(optimizer='adam', loss=length_penalty_loss)

# Train the model (assuming x_train and y_train are defined)
# model.fit(x_train, y_train, epochs=10, batch_size=64)

🚀 Reparameterization Trick in Reinforcement Learning - Made Simple!

The reparameterization trick is also useful in reinforcement learning, particularly for continuous action spaces. Here’s an example of how it can be used in a policy gradient method:

Let’s make this super clear! Here’s how we can tackle this:

import tensorflow as tf
import tensorflow_probability as tfp

class ContinuousPolicy(tf.keras.Model):
    def __init__(self, state_dim, action_dim):
        super(ContinuousPolicy, self).__init__()
        self.dense1 = tf.keras.layers.Dense(64, activation='relu')
        self.dense2 = tf.keras.layers.Dense(64, activation='relu')
        self.mean = tf.keras.layers.Dense(action_dim)
        self.log_std = tf.keras.layers.Dense(action_dim)

    def call(self, state):
        x = self.dense1(state)
        x = self.dense2(x)
        mean = self.mean(x)
        log_std = self.log_std(x)
        return mean, log_std

    def sample_action(self, state):
        mean, log_std = self(state)
        std = tf.exp(log_std)
        normal_dist = tfp.distributions.Normal(mean, std)
        action = normal_dist.sample()
        log_prob = normal_dist.log_prob(action)
        return action, log_prob

# Example usage in a reinforcement learning algorithm
policy = ContinuousPolicy(state_dim=4, action_dim=2)
optimizer = tf.keras.optimizers.Adam(learning_rate=0.001)

@tf.function
def train_step(states, actions, rewards):
    with tf.GradientTape() as tape:
        _, log_probs = policy.sample_action(states)
        loss = -tf.reduce_mean(log_probs * rewards)  # Policy gradient loss
    
    gradients = tape.gradient(loss, policy.trainable_variables)
    optimizer.apply_gradients(zip(gradients, policy.trainable_variables))
    return loss

# Main training loop (pseudo-code)
# for episode in range(num_episodes):
#     states, actions, rewards = collect_episode_data()
#     loss = train_step(states, actions, rewards)
#     print(f"Episode {episode}, Loss: {loss.numpy()}")

🚀 Bayes’ Theorem in Anomaly Detection - Made Simple!

Bayes’ theorem can be applied to anomaly detection tasks, where we want to identify unusual patterns in data. Here’s an example of a simple Bayesian anomaly detector:

Here’s a handy trick you’ll love! Here’s how we can tackle this:

import numpy as np
from scipy.stats import norm

class BayesianAnomalyDetector:
    def __init__(self, prior_prob_anomaly=0.01):
        self.prior_prob_anomaly = prior_prob_anomaly
        self.normal_params = {}
        self.anomaly_params = {}

    def fit(self, X):
        # Estimate parameters for normal data
        self.normal_params['mean'] = np.mean(X, axis=0)
        self.normal_params['std'] = np.std(X, axis=0)
        
        # Assume anomalies have wider distribution
        self.anomaly_params['mean'] = self.normal_params['mean']
        self.anomaly_params['std'] = 3 * self.normal_params['std']

    def predict(self, X):
        likelihood_normal = norm.pdf(X, self.normal_params['mean'], self.normal_params['std'])
        likelihood_anomaly = norm.pdf(X, self.anomaly_params['mean'], self.anomaly_params['std'])
        
        prior_normal = 1 - self.prior_prob_anomaly
        evidence = (likelihood_normal * prior_normal + 
                    likelihood_anomaly * self.prior_prob_anomaly)
        
        posterior_prob_anomaly = (likelihood_anomaly * self.prior_prob_anomaly) / evidence
        
        return posterior_prob_anomaly > 0.5

# Example usage
np.random.seed(42)
normal_data = np.random.normal(0, 1, (1000, 2))
anomaly_data = np.random.normal(3, 2, (50, 2))
X = np.vstack([normal_data, anomaly_data])

detector = BayesianAnomalyDetector()
detector.fit(normal_data)

predictions = detector.predict(X)
print(f"Detected {np.sum(predictions)} anomalies out of {len(X)} data points")

# Visualize results
import matplotlib.pyplot as plt
plt.figure(figsize=(10, 6))
plt.scatter(X[~predictions, 0], X[~predictions, 1], label='Normal')
plt.scatter(X[predictions, 0], X[predictions, 1], color='red', label='Anomaly')
plt.title('Bayesian Anomaly Detection')
plt.legend()
plt.show()

🚀 ELBO Loss in Topic Modeling - Made Simple!

The Evidence Lower Bound (ELBO) loss is often used in topic modeling, particularly in Latent Dirichlet Allocation (LDA) variants. Here’s a simplified implementation of a neural topic model using ELBO loss:

Here’s where it gets exciting! Here’s how we can tackle this:

import tensorflow as tf
import tensorflow_probability as tfp

class NeuralTopicModel(tf.keras.Model):
    def __init__(self, vocab_size, num_topics):
        super(NeuralTopicModel, self).__init__()
        self.vocab_size = vocab_size
        self.num_topics = num_topics
        
        self.encoder = tf.keras.Sequential([
            tf.keras.layers.Dense(256, activation='relu'),
            tf.keras.layers.Dense(128, activation='relu'),
            tf.keras.layers.Dense(num_topics * 2)
        ])
        
        self.decoder = tf.keras.layers.Dense(vocab_size)

    def encode(self, x):
        params = self.encoder(x)
        mu, log_sigma = tf.split(params, 2, axis=-1)
        return mu, log_sigma

    def reparameterize(self, mu, log_sigma):
        eps = tf.random.normal(shape=mu.shape)
        return mu + tf.exp(log_sigma) * eps

    def decode(self, z):
        return self.decoder(z)

    def call(self, inputs):
        mu, log_sigma = self.encode(inputs)
        z = self.reparameterize(mu, log_sigma)
        return self.decode(z), mu, log_sigma

def elbo_loss(model, x):
    reconstructed, mu, log_sigma = model(x)
    
    # Reconstruction loss
    rec_loss = tf.reduce_sum(
        tf.nn.sigmoid_cross_entropy_with_logits(logits=reconstructed, labels=x),
        axis=-1
    )
    
    # KL divergence
    kl_loss = -0.5 * tf.reduce_sum(
        1 + 2 * log_sigma - tf.square(mu) - tf.exp(2 * log_sigma),
        axis=-1
    )
    
    return tf.reduce_mean(rec_loss + kl_loss)

# Example usage
vocab_size = 10000
num_topics = 20
model = NeuralTopicModel(vocab_size, num_topics)
optimizer = tf.keras.optimizers.Adam()

@tf.function
def train_step(x):
    with tf.GradientTape() as tape:
        loss = elbo_loss(model, x)
    gradients = tape.gradient(loss, model.trainable_variables)
    optimizer.apply_gradients(zip(gradients, model.trainable_variables))
    return loss

# Assuming x_train is your document-term matrix
# for epoch in range(num_epochs):
#     for batch in x_train:
#         loss = train_step(batch)
#     print(f"Epoch {epoch + 1}, Loss: {loss.numpy():.4f}")

🚀 Additional Resources - Made Simple!

For those interested in diving deeper into these topics, here are some valuable resources:

1. “Variational Inference: A Review for Statisticians” by David M. Blei, Alp Kucukelbir, and Jon D. McAuliffe (2017) ArXiv: https://arxiv.org/abs/1601.00670
2. “Auto-Encoding Variational Bayes” by Diederik P. Kingma and Max Welling (2013) ArXiv: https://arxiv.org/abs/1312.6114
3. “Attention Is All You Need” by Ashish Vaswani et al. (2017) ArXiv: https://arxiv.org/abs/1706.03762
4. “Deep Reinforcement Learning: An Overview” by Yuxi Li (2017) ArXiv: https://arxiv.org/abs/1701.07274
5. “A Tutorial on Bayesian Optimization” by Peter I. Frazier (2018) ArXiv: https://arxiv.org/abs/1807.02811

These papers provide in-depth explanations and mathematical foundations for many of the concepts we’ve discussed in this presentation. They are excellent starting points for further exploration in machine learning, deep learning, and probabilistic modeling.

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🎊 Awesome Work!

You’ve just learned some really powerful techniques! Don’t worry if everything doesn’t click immediately - that’s totally normal. The best way to master these concepts is to practice with your own data.

What’s next? Try implementing these examples with your own datasets. Start small, experiment, and most importantly, have fun with it! Remember, every data science expert started exactly where you are right now.

Keep coding, keep learning, and keep being awesome! 🚀