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AL-503 (A) · Information Retrieval/Quick Revision Short Notes

Information Retrieval (AL-503 (A)) - Unit 4 Short Notes

UNIT 4: Advanced Information Retrieval and Deep Learning

1. Fundamentals of Information Retrieval

1.1 Information Retrieval Process and Key Components

  • Process: Query → Index lookup → Ranking → Results presentation.

  • Key Components:

    • Document Collection: Corpus of text/data.

    • Index: Inverted index for fast lookup.

    • Query Processor: Parses and transforms user queries.

    • Ranking Algorithm: Scores documents (e.g., TF-IDF, BM25).

    • User Interface: Displays results with snippets.

[!TIP] Exam focus: Diagram the IR pipeline and explain each component's role.

1.2 Traditional IR Systems vs Web Search

Aspect Traditional IR Web Search
Scale Small, curated collections Billions of pages, dynamic
Structure Mostly unstructured text HTML with links, metadata
Algorithms Boolean, vector space PageRank, anchor text, spam detection
Challenges Vocabulary mismatch Duplicate content, link spam

1.3 Role of Artificial Intelligence in IR

  • Query Understanding: NLP for intent detection, expansion.

  • Ranking: Learning to Rank (LTR) models (e.g., LambdaRank).

  • User Modeling: Personalization via collaborative filtering.

  • Example: BERT for semantic matching between query and document.


2. Document and Query Processing

2.1 Document Preprocessing Procedures

  1. Tokenization: Split text into words/terms.

  2. Stop Word Removal: Eliminate common words (e.g., "the", "is").

  3. Stemming/Lemmatization: Reduce to root form (e.g., "running" → "run").

  4. Normalization: Case folding, accent removal.

2.2 Term Weighting: TF-IDF

  • Term Frequency (TF): Frequency of term in document.

$$ \text{tf}(t,d) = \frac{f_{t,d}}{\sum_{t' \in d} f_{t',d}} $$

  • Inverse Document Frequency (IDF): Downweight frequent terms.

$$ \text{idf}(t) = \log\left(\frac{N}{\text{df}(t)}\right) $$

  • TF-IDF Score:

$$ \text{TF-IDF}(t,d) = \text{tf}(t,d) \times \text{idf}(t) \boxed{} $$

[!TIP] IDF reduces impact of common words; higher score = more important term in document.

2.3 Index Compression (Benefits with Examples)

  • Need: Reduce storage, improve I/O speed.

  • Techniques:

    • Gamma Encoding: For gaps between document IDs.

    • Variable-Byte Encoding: Byte-aligned compression.

  • Example: Store gaps [5, 12, 3] instead of IDs [10, 22, 25].

  • Benefit: 50-70% space reduction; faster disk reads.

2.4 Snippet Generation

  • Static Snippets: Precomputed from document (e.g., first 100 words).

  • Dynamic Snippets: Query-dependent; extract sentences containing query terms.

  • Algorithm: Identify query term positions, return surrounding context (e.g., 20 words before/after).

[!TIP] Dynamic snippets improve relevance but increase computation.


3. Retrieval Models and Techniques

3.1 Vector Space Model and Ranking Procedures

  • Documents and queries as vectors in term space.

  • Ranking: Cosine similarity between query vector $\vec{q}$ and document vector $\vec{d}$:

$$ \text{score}(q,d) = \frac{\vec{q} \cdot \vec{d}}{||\vec{q}|| \cdot ||\vec{d}||} $$

  • Weighting: Typically TF-IDF.

3.2 Probabilistic Relevance Feedback

  • Rocchio Algorithm: Update query vector using relevant/non-relevant docs.

$$ \vec{q}_{\text{new}} = \alpha \vec{q} + \beta \frac{1}{|D_r|} \sum_{\vec{d} \in D_r} \vec{d} - \gamma \frac{1}{|D_{nr}|} \sum_{\vec{d} \in D_{nr}} \vec{d} $$

where $$\displaystyle D_r $$ = relevant docs, $$\displaystyle D_{nr} $$ = non-relevant.

  • Goal: Move query toward relevant documents in vector space.

3.3 Latent Semantic Indexing (LSI) with Examples

  • Idea: Use SVD to find latent topics (lower-dimensional space).

  • Steps:

    1. Build term-document matrix $A$.

    2. Compute SVD: $$\displaystyle A = U \Sigma V^T $$.

    3. Truncate to $k$ dimensions: $$\displaystyle A_k = U_k \Sigma_k V_k^T $$.

  • Example: Words "car", "automobile" map to same latent topic.

  • Benefit: Handles synonymy, polysemy.

3.4 Retrieval Using Ranking and Relative Scores

  • BM25: Probabilistic model with term frequency saturation and document length normalization.

$$ \text{score}(D,Q) = \sum_{t \in Q} \text{idf}(t) \cdot \frac{f(t,D) \cdot (k_1 + 1)}{f(t,D) + k_1 \cdot \left(1 - b + b \cdot \frac{|D|}{\text{avgdl}}\right)} $$

  • Relative Scores: Combine multiple signals (e.g., BM25 + PageRank) via linear combination or learning to rank.

4. Web Information Retrieval

4.1 Web Crawlers: Advantages, Needs, and Focused Crawling

  • Needs:

    • Scale: Discover billions of pages.

    • Freshness: Update changed content.

    • Politeness: Respect robots.txt, avoid overload.

  • Advantages: Build search engine index, monitor web changes.

  • Focused Crawling: Target specific topics (e.g., "machine learning").

    • Strategy: Use classifier to predict relevance of links; prioritize promising URLs.

    • Example: Use BFS with priority queue based on page relevance score.

4.2 XML Information Retrieval System Requirements

  • Structural Queries: Support XPath/XQuery for nested elements.

  • Element Retrieval: Return specific XML fragments (not whole docs).

  • Ranking: Combine text relevance with structural similarity (e.g., tag weights).

  • Indexing: Inverted index on element text + structural index (e.g., region encoding).

4.3 Large-Scale IR: MapReduce and Hadoop Implementation

  • Map Phase: Process document chunks → emit (term, docID) pairs.

  • Shuffle/Sort: Group by term.

  • Reduce Phase: For each term, merge docIDs → postings list.

  • Example: Inverted index construction:

    • Map: Input split → (term, 1) for each occurrence.

    • Reduce: Sum counts → (term, [(docID, freq)]).

  • Benefit: Parallelizable, fault-tolerant; handles petabytes.


5. Machine Learning for Information Retrieval

5.1 Supervised vs Unsupervised Learning (with Examples)

Supervised Unsupervised
Labeled data (input-output) No labels
Examples: Classification (spam detection), Regression (CTR prediction). Examples: Clustering (grouping docs), Dimensionality reduction (LSI).

5.2 Classification Techniques

5.2.1 Naive Bayesian Classification and Limitations

  • Bayes' Theorem: $$\displaystyle P(C|D) \propto P(C) \prod_{t \in D} P(t|C) $$.

  • Assumption: Features (words) conditionally independent.

  • Limitations:

    • Independence assumption often violated.

    • Zero probability problem (solved by Laplace smoothing).

    • Poor with correlated features.

5.2.2 Logistic Regression

  • Model: $$\displaystyle P(y=1|x) = \frac{1}{1 + e^{-(w^T x + b)}} $$.

  • Training: Maximize log-likelihood via gradient descent.

  • Use: Binary classification (e.g., relevant/not relevant).

  • Advantage: Probabilistic output, interpretable weights.

5.2.3 k-Nearest Neighbors (Choosing K)

  • Algorithm: For a query, find K most similar training instances; majority vote.

  • Choosing K:

    • Elbow Method: Plot accuracy vs K; choose point of diminishing returns.

    • Cross-Validation: Test different K on validation set.

    • Rule of Thumb: $K \approx \sqrt{N}$ (N = samples).

  • Distance Metric: Euclidean, cosine similarity.

5.3 Clustering Techniques

5.3.1 Agglomer Clustering

  • Bottom-up: Start each doc as cluster; merge closest pairs.

  • Linkage Criteria:

    • Single: min distance between clusters.

    • Complete: max distance.

    • Average: average pairwise distance.

  • Stopping: Predefined number of clusters or distance threshold.

5.3.2 k-Means Clustering (Choosing K)

  • Algorithm:

    1. Initialize K centroids.

    2. Assign points to nearest centroid.

    3. Update centroids as mean of assigned points.

    4. Repeat until convergence.

  • Objective:

$$ J = \sum_{i=1}^{k} \sum_{x \in C_i} ||x - \mu_i||^2 \boxed{} $$

  • Choosing K: Elbow method (plot J vs K), silhouette score.

5.4 Dimensionality Reduction

5.4.1 PCA/SVD vs Autoencoders

PCA/SVD Autoencoders
Linear transformation Non-linear (with deep networks)
Global structure Can learn complex manifolds
Computationally cheaper Requires training, more flexible
Use: Quick compression, LSI Use: Complex data (images, text)

5.4.2 Autoencoders: Sparse, Contractive, Variational

  • Sparse Autoencoder: Add sparsity constraint on hidden units (e.g., L1 penalty).

  • Contractive Autoencoder: Penalize Jacobian norm → robust features.

  • Variational Autoencoder (VAE): Probabilistic; learns latent distribution (see Section 7.6).

5.5 Recommendation Systems

5.5.1 Content-Based Recommendation Systems

  • Idea: Recommend items similar to user's past likes based on item features.

  • Steps:

    1. Build user profile from liked items (e.g., TF-IDF vector of item descriptions).

    2. Compute similarity between user profile and candidate items.

    3. Rank and recommend top-N.

  • Advantage: No cold-start for new items; transparent.

  • Limitation: Overspecialization, limited by item features.


6. Deep Learning Fundamentals

6.1 Historical Progression and Key Milestones

  • 1940s-50s: Perceptron (Rosenblatt).

  • 1980s: Backpropagation (Rumelhart, Hinton).

  • 2006: Deep Belief Networks (Hinton) → deep learning renaissance.

  • 2012: AlexNet (ReLU, dropout, GPU) wins ImageNet.

  • 2014-: GANs, VAEs, transformers.

6.2 Neural Network Basics

6.2.1 Architecture of Simple and Deep Feedforward Networks

  • Simple: Input layer → Hidden layer(s) → Output layer.

  • Deep: Multiple hidden layers (≥2).

  • Fully Connected: Each neuron connected to all in next layer.

  • Example: MLP for classification: Input (features) → Hidden (ReLU) → Output (softmax).

6.2.2 Activation Functions: Importance and Types

Function Formula Pros Cons
Sigmoid $$\displaystyle \sigma(x) = \frac{1}{1+e^{-x}} $$ Smooth, output (0,1) Vanishing gradient, not zero-centered
Tanh $\tanh(x)$ Zero-centered, steeper than sigmoid Vanishing gradient
ReLU $\max(0,x)$ Non-saturating, fast computation Dying ReLU (negative gradient)
Leaky ReLU $\max(\alpha x, x)$, $\alpha$ small Fixes dying ReLU May not generalize well

[!TIP] ReLU most common in hidden layers; softmax for multi-class output.

6.2.3 Representation Power of MLPs and Sigmoid Neurons

  • Universal Approximation Theorem: MLP with one hidden layer (sigmoid/tanh) can approximate any continuous function given enough neurons.

  • Deep vs Shallow: Deep networks learn hierarchical features more efficiently (fewer parameters).

6.3 Training Neural Networks

6.3.1 Backpropagation Algorithm

  1. Forward Pass: Compute output and loss.

  2. Backward Pass:

    • Compute gradient of loss w.r.t. each weight via chain rule.

    • Update weights: $$\displaystyle w \leftarrow w - \eta \frac{\partial \mathcal{L}}{\partial w} $$.

[!TIP] Key: Compute local gradients at each layer; store activations during forward pass.

6.3.2 Optimization Algorithms

Algorithm Key Idea Use Case
SGD $$\displaystyle \Delta w = -\eta \nabla \mathcal{L} $$ Simple, noisy convergence
AdaGrad Adapt learning rate per parameter (accumulate squares of gradients) Sparse data
RMSProp Running average of squared gradients Non-stationary objectives
Adam Combine momentum and RMSProp (adaptive LR) Default choice, robust

6.3.3 Challenges: Vanishing and Exploding Gradients (BPTT)

  • Vanishing: Gradients → 0 in early layers (sigmoid/tanh); weights stop updating.

  • Exploding: Gradients → large; unstable training.

  • Mitigation:

    • ReLU and variants.

    • Batch Normalization.

    • Residual Connections (skip connections).

    • Gradient Clipping (for exploding).

[!TIP] Common in deep networks and RNNs (BPTT); use LSTM/GRU for RNNs.

6.4 Regularization Techniques

6.4.1 Overfitting and Underfitting

  • Overfitting: Model fits noise; high train accuracy, low test accuracy.

  • Underfitting: Model too simple; low train/test accuracy.

  • Diagnosis: Learning curves (train vs validation loss).

6.4.2 Dropout

  • Mechanism: Randomly set fraction $p$ of hidden units to 0 during training.

  • Inference: Scale weights by $(1-p)$ or use inverted dropout.

  • Effect: Prevents co-adaptation; ensemble effect.

  • Typical $p$: 0.5 for hidden layers, 0.2 for input.

6.4.3 Weight Decay

  • L2 Regularization: Add $$\displaystyle \frac{\lambda}{2} ||w||^2 $$ to loss.

  • Update: $$\displaystyle w \leftarrow w - \eta (\nabla \mathcal{L} + \lambda w) $$.

  • Effect: Penalizes large weights; smoother function.

6.4.4 Batch Normalization (How it Works and Advantages)

  • How:

    1. For mini-batch, compute mean $$\displaystyle \mu_B $$ and variance $$\displaystyle \sigma_B^2 $$.

    2. Normalize: $$\displaystyle \hat{x}^{(i)} = \frac{x^{(i)} - \mu_B}{\sqrt{\sigma_B^2 + \epsilon}} $$.

    3. Scale and shift: $$\displaystyle y^{(i)} = \gamma \hat{x}^{(i)} + \beta $$.

  • Advantages:

    • Reduces internal covariate shift.

    • Allows higher learning rates.

    • Acts as regularizer (noise from batch statistics).

[!TIP] Applied before activation; use learned $\gamma,\beta$.

6.5 Data Preprocessing

6.5.1 Normalization vs Standardization

Normalization (Min-Max) Standardization (Z-score)
$$\displaystyle x' = \frac{x - \min}{\max - \min} $$ $$\displaystyle x' = \frac{x - \mu}{\sigma} $$
Scales to [0,1] Zero mean, unit variance
Sensitive to outliers Robust to outliers
Use: Image pixels, bounded features Use: Most deep learning, when data not bounded

7. Deep Learning Architectures

7.1 Convolutional Neural Networks (CNNs)

7.1.1 Architecture and Role in Image Recognition

  • Layers:

    • Convolutional: Apply filters to extract features (edges, textures).

    • Pooling: Downsample (max/average pooling).

    • Fully Connected: At end for classification.

  • Role: Translation invariance, parameter sharing (efficient for images).

7.1.2 Key Terms: Padding and Pooling

  • Padding: Add zeros around input to control output size.

    • Same Padding: Output size = input size.

    • Valid Padding: No padding; output shrinks.

  • Pooling: Reduce spatial dimensions, increase receptive field.

    • Max Pooling: Take maximum in window (common).

    • Average Pooling: Average values.

[!TIP] Pooling provides translation invariance; stride controls downsampling.

7.1.3 Data Formats for CNNs (Examples)

Data Type Format (Tensor) Example Shape
Image (RGB) (Height, Width, Channels) (224, 224, 3)
Video (Frames, Height, Width, Channels) (30, 224, 224, 3)
Text (1D conv) (Sequence Length, Features) (500, 300) for 500 words with 300-dim embeddings
Spectrogram (Time, Frequency, Channels) (128, 128, 1) for audio

[!TIP] CNNs can handle 1D (text), 2D (images), 3D (video) data.

7.2 Recurrent Neural Networks (RNNs)

7.2.1 Architecture and Handling Sequential Data

  • Architecture: Hidden state $$\displaystyle h_t $$ depends on previous state $$\displaystyle h_{t-1} $$ and input $$\displaystyle x_t $$:

$$ h_t = f(W_{hh} h_{t-1} + W_{xh} x_t + b_h) $$

  • Handles Sequences: Processes one time step at a time; maintains memory.

  • Use: Language modeling, time series.

7.2.2 Deep RNNs and Architectures

  • Deep RNNs: Stack multiple RNN layers.

    • Layer 1: $$\displaystyle h_t^{(1)} = f(W^{(1)} [h_{t-1}^{(1)}, x_t] + b^{(1)}) $$

    • Layer 2: $$\displaystyle h_t^{(2)} = f(W^{(2)} [h_{t-1}^{(2)}, h_t^{(1)}] + b^{(2)}) $$

  • Bidirectional RNNs: Process sequence forward and backward; concatenate hidden states.

  • Architectures: Many-to-one (sentiment), one-to-many (captioning), many-to-many (machine translation).

7.2.3 Backpropagation Through Time (BPTT) Challenges

  • Unfolding: RNN unrolled for T time steps.

  • Challenges:

    • Vanishing/Exploding Gradients: Gradients multiplied by same weight matrix repeatedly.

    • Long-Term Dependencies: Gradients from distant time steps vanish.

  • Mitigation: LSTM/GRU, gradient clipping, proper initialization.

7.3 Long Short-Term Memory (LSTM)

7.3.1 Detailed Working Mechanism

DiagramCANVAS: LSTM cell with input gate $$\displaystyle i_t $$, forget gate $$\displaystyle f_t $$, output gate $$\displaystyle o_t $$, cell state $$\displaystyle C_t $$, hidden state $$\displaystyle h_t $$. Arrows show flow and equations: $$\displaystyle f_t = \sigma(W_f \cdot [h_{t-1}, x_t] + b_f) $$; $$\displaystyle i_t = \sigma(W_i \cdot [h_{t-1}, x_t] + b_i) $$; $$\displaystyle \tilde{C}_t = \tanh(W_C \cdot [h_{t-1}, x_t] + b_C) $$; $$\displaystyle C_t = f_t \odot C_{t-1} + i_t \odot \tilde{C}_t $$; $$\displaystyle o_t = \sigma(W_o \cdot [h_{t-1}, x_t] + b_o) $$; $$\displaystyle h_t = o_t \odot \tanh(C_t) $$.
  • Gates:

    • Forget Gate: Decides what to discard from cell state.

    • Input Gate: Updates cell state with new information.

    • Output Gate: Produces hidden state from cell state.

  • Cell State $$\displaystyle C_t $$: Linear path; mitigates vanishing gradient.

7.3.2 Advantages over Standard RNNs

  • Handles long-term dependencies (cell state acts as memory).

  • Solves vanishing gradient problem (additive updates).

  • Flexible gating allows learning when to forget/remember.

7.4 Recursive Neural Networks

  • Architecture: Tree-structured; same neural net applied in a recursive manner.

  • Process: Leaf nodes (words) → combine via parent node → root.

  • Use: Parsing, sentiment analysis (captures hierarchical structure).

  • Difference from RNN: RNNs sequential; recursive neural networks tree-based.

[!TIP] Requires parse tree; less common than RNNs/LSTMs for sequence data.

7.5 Autoencoders

7.5.1 Types: Sparse, Contractive, Variational

  • Sparse: Hidden layer activations penalized (L1 loss) → few active neurons.

  • Contractive: Penalize Jacobian norm $$\displaystyle \left\| \frac{\partial h}{\partial x} \right\|^2 $$ → robust to input perturbations.

  • Variational (VAE): See Section 7.6.2.

7.5.2 Regularization in Autoencoders

  • Why: Prevent trivial identity mapping; force learning meaningful representations.

  • Methods:

    • Sparsity constraint: Encourage few active units.

    • Denoising autoencoder: Train to reconstruct clean input from corrupted version.

    • Contractive penalty: As above.

7.5.3 Applications in Dimensionality Reduction

  • Process: Encoder maps high-dim input to low-dim latent code; decoder reconstructs.

  • Vs PCA: Non-linear; can learn complex manifolds.

  • Use: Pre-training for deep networks, anomaly detection, generative modeling (VAE).

7.6 Generative Models

7.6.1 Generative Adversarial Networks (GANs)

  • Architecture:

    • Generator $G$: Takes noise $z$ → generates fake data $G(z)$.

    • Discriminator $D$: Classifies real vs fake.

  • Training: Minimax game:

$$ \min_G \max_D V(D,G) = \mathbb{E}_{x\sim p_{data}}[\log D(x)] + \mathbb{E}_{z\sim p_z}[\log(1-D(G(z)))] \boxed{} $$

  • Use: Image generation, style transfer.

7.6.2 Variational Autoencoders (VAEs)

  • Idea: Learn probabilistic latent variable model.

  • Encoder: Outputs parameters $(\mu, \sigma)$ of latent distribution $q(z|x)$.

  • Decoder: Reconstructs $x$ from sampled $z$.

  • Loss (ELBO):

$$ \mathcal{L} = \mathbb{E}_{q(z|x)}[\log p(x|z)] - D_{KL}(q(z|x) || p(z)) \boxed{} $$

  • Use: Smooth latent space, interpolation.

7.6.3 Comparison and Use Cases

Aspect GANs VAEs
Training Unstable, mode collapse Stable, convergent
Output Quality Sharp, realistic images Blurry, averaged
Latent Space Disentangled? (not guaranteed) Structured, continuous
Use When High-fidelity generation (faces) Interpolation, controlled generation, semi-supervised learning

8. Advanced Deep Learning Concepts

8.1 Representation Learning

  • Goal: Learn features automatically from raw data (instead of manual feature engineering).

  • Methods: Autoencoders, deep networks, contrastive learning.

  • Benefit: Captures hierarchical patterns; improves performance on downstream tasks.

8.2 Deep Belief Networks

  • Structure: Stack of Restricted Boltzmann Machines (RBMs).

  • Training: Greedy layer-wise pretraining (unsupervised) → fine-tune with backprop.

  • Use: Early deep learning for initialization; now largely superseded by better initialization (He, Xavier) and ReLU.

8.3 Auto-regressive Models: NADE and MADE

  • Idea: Model density $p(x)$ as product of conditionals: $$\displaystyle p(x) = \prod_{i=1}^d p(x_i | x_{<i}) $$.

  • NADE (Neural Autoregressive Density Estimator): Single hidden layer with masked connections to ensure autoregressive property.

  • MADE (Masked Autoencoder for Distribution Estimation): Extends NADE to deep networks; masks enforce dependency order.

  • Use: Density estimation, generative modeling.

8.4 Model Compression and Pruning

8.4.1 Unit Pruning

  • Idea: Remove entire neurons/filters with small impact on output.

  • Method:

    1. Train large network.

    2. Evaluate importance (e.g., magnitude of weights, activation frequency).

    3. Prune least important units.

    4. Fine-tune remaining network.

  • Benefit: Reduces parameters, inference speed; minimal accuracy loss.

[!TIP] Structured pruning (whole filters) more efficient for hardware than unstructured.

8.5 Visualization Techniques

8.5.1 Deep Dream

  • Process: Modify input image to maximize activations of specific layers/filters.

  • Algorithm:

    1. Forward pass; compute gradient of loss (activation) w.r.t. input.

    2. Update input in gradient ascent direction.

    3. Repeat.

  • Result: Surreal, enhanced patterns; reveals what filters "see".

  • Use: Interpretability, art.

8.6 Graphical Models

8.6.1 Directed Graphical Models

  • Definition: Bayesian networks; nodes = random variables, edges = conditional dependencies.

  • Factorization: Joint probability $$\displaystyle p(x_1,...,x_n) = \prod_{i=1}^n p(x_i | \text{parents}(x_i)) $$.

  • Example: Naive Bayes is a directed graph (class → features).

  • Use: Probabilistic reasoning, causal inference.


9. Deep Learning for Sequential Data and Decision Making

9.1 Advanced RNNs for Long-Range Dependencies

  • GRUs: Gated Recurrent Units; simpler than LSTM (reset and update gates).

  • Attention Mechanism: Allow decoder to attend to all encoder states (Transformer).

  • Layer Normalization: Stabilize RNN training.

  • Use: Machine translation, speech recognition.

9.2 Reinforcement Learning Foundations

9.2.1 Markov Decision Processes (MDPs)

  • Components:

    • States $S$, Actions $A$, Transition $P(s'|s,a)$, Reward $R(s,a,s')$, Discount $\gamma$.

    • Policy $\pi(a|s)$: Probability of action in state.

  • Goal: Maximize expected discounted return $$\displaystyle G_t = \sum_{k=0}^\infty \gamma^k R_{t+k+1} $$.

9.2.2 Value Iteration and Policy Iteration (Comparison)

  • Value Iteration:

    • Update value function until convergence: $$\displaystyle V_{k+1}(s) = \max_a \sum_{s'} P(s'|s,a) [R(s,a,s') + \gamma V_k(s')] $$.

    • Pros: Simple, no policy evaluation step.

    • Cons: Slower per iteration (full backup).

  • Policy Iteration:

    1. Policy Evaluation: Compute $$\displaystyle V^\pi $$ for current policy $\pi$ (solve linear system).

    2. Policy Improvement: Update policy greedily: $$\displaystyle \pi'(s) = \arg\max_a \sum_{s'} P(s'|s,a)[R + \gamma V^\pi(s')] $$.

    • Pros: Faster convergence per iteration.

    • Cons: Policy evaluation expensive for large state spaces.

[!TIP] Value iteration used in model-based RL; policy iteration in dynamic programming.

9.3 Deep Reinforcement Learning

9.3.1 Q-Learning and Deep Q-Networks (DQN)

  • Q-Learning: Learn action-value function $Q(s,a)$.

    • Update: $$\displaystyle Q(s,a) \leftarrow Q(s,a) + \alpha [r + \gamma \max_{a'} Q(s',a') - Q(s,a)] $$.
  • DQN:

    • Use deep network to approximate $Q(s,a;\theta)$.

    • Key tricks:

      • Experience Replay: Store transitions $(s,a,r,s')$; sample mini-batches.

      • Target Network: Separate network for target $$\displaystyle y = r + \gamma \max_{a'} Q(s',a';\theta^-) $$; update slowly.

    • Loss:

$$ L(\theta) = \mathbb{E}_{(s,a,r,s') \sim U(D)} \left[ \left( r + \gamma \max_{a'} Q(s',a';\theta^-) - Q(s,a;\theta) \right)^2 \right] \boxed{} $$

9.3.2 Advanced DQN Variants

  • Double DQN: Decouple action selection and evaluation to reduce overestimation.

$$ y = r + \gamma Q(s', \arg\max_{a'} Q(s',a';\theta); \theta^-) $$

  • Dueling DQN: Separate streams for value $V(s)$ and advantage $A(s,a)$:

$$ Q(s,a) = V(s) + A(s,a) - \frac{1}{|\mathcal{A}|} \sum_{a'} A(s,a') $$

9.3.3 Least Squares Methods: LSPI

  • LSPI (Least Squares Policy Iteration):

    • Use least-squares to fit $Q(s,a)$ from samples (instead of gradient descent).

    • Steps:

      1. Collect dataset with current policy.

      2. Solve linear system for $Q$ weights (using basis functions).

      3. Improve policy greedily.

    • Advantage: Sample efficiency; converges in few iterations.

    • Disadvantage: Requires matrix inversion; costly for large problems.

9.3.4 Deep RL Applications

  • Games: AlphaGo (policy + value networks), DQN for Atari.

  • Robotics: Policy gradient methods (PPO) for control.

  • Recommendation: Multi-armed bandits for personalization.


10. Integration of Deep Learning in IR Systems

10.1 Neural Networks for Ranking (Learning to Rank)

  • Pointwise: Treat ranking as regression/classification on individual documents (e.g., $\text{score}(q,d)$).

  • Pairwise: Learn to compare document pairs (e.g., RankNet: logistic loss on $$\displaystyle P(d_i \succ d_j|q) $$).

  • Listwise: Optimize ranking metric directly (e.g., LambdaRank, ListNet).

[!TIP] LTR features: Traditional (TF-IDF) + deep (BERT embeddings).

10.2 CNNs for Image and Multimodal Retrieval

  • Image Retrieval: CNN (e.g., ResNet) extracts feature vectors; compare via cosine similarity.

  • Multimodal: Joint embedding space (e.g., CNN for image, LSTM for text); train with contrastive loss.

  • Example: Cross-modal retrieval: query text → retrieve images.

10.3 RNNs/LSTMs for Text Retrieval and Query Understanding

  • Query Understanding: LSTMs encode query into vector; capture intent, context.

  • Session Modeling: RNNs model user's sequential interactions for next-query prediction.

  • Use in IR: Re-ranking with semantic similarity (e.g., match query and doc vectors).

10.4 Deep Learning in Recommendation Systems

  • Neural Collaborative Filtering (NCF): Replace matrix factorization with neural network on user/item embeddings.

  • Sequence-aware: Use RNNs/Transformers to model user interaction history (e.g., SASRec).

  • Multimodal: Combine text (BERT), images (CNN) for item representation.

10.5 Challenges and Future Directions

  • Challenges:

    • Data Sparsity: Few user-item interactions.

    • Scalability: Real-time inference for millions of items.

    • Interpretability: Black-box models.

    • Cold Start: New users/items.

  • Future Directions:

    • Self-supervised learning for pre-training.

    • Causal inference for recommendations.

    • Federated learning for privacy.

    • Efficient transformers for long sequences.

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