Final review post for csci-331

blogContent/posts/data-science/csci-331-final-review.md

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+Quick review sheet for Dr. Homan's RIT CSCI-331 final.
+
+# Learning from examples (Ch 18)
+
+- Supervised learning: where you already know the answers
+- Re-enforcement learning: Learning with rewards
+- Unsupervised: clustering
+
+
+![](media/final/learningAgent.PNG)
+
+## Inductive learning problems
+
+![](media/final/inductiveLearning.PNG)
+
+![](media/final/ock.PNG)
+
+Ockham's razor: Maximize a combination of consistency and simplicity.
+Often times overly complex models that perfectly fit the training data does not generalize well for new data.
+
+
+## Decision trees
+
+Often the most natural way of representing a boolean problem, but, don't often generalize well.
+
+![](media/final/decisionTree.PNG)
+
+## Entropy
+
+Decision trees use entropy to pick which input to branch on first.
+A 50/50 split in data is usually less useful than a 80/20 split in data because the 50/50 split still has more "information" in it.
+We pick the input that minimizes entropy.
+
+$$
+entropy = \sum^n_{i = 1} -P_i log_2 P_i
+$$
+
+## Neural networks
+
+Based on human brains.
+
+
+McCullon-Pitts
+
+![](media/final/pitts.PNG)
+
+Examples of logic functions:
+
+![](media/final/logicNeurons.PNG)
+
+### Single Layer Perceptrons
+
+![](media/final/singleLayer.PNG)
+
+### Multi-layer Perceptrons
+
+![](media/final/multiLayer.PNG)
+
+
+## Backpropagation
+
+Way of incrementally adjusting the weights so that the model better fits the training data.
+
+
+## SVMs: Support Vector Machine
+
+- very high dimensions
+- as long as data is sparse, the curse of dimensionality is not an issue
+- By default it assumes you can linearly separate the data if you can use a large amount of dimensions. Sometimes you use something called the kernel trick to distort the space to make the data linearly separable.
+
+![](media/final/svm.PNG)
+
+## CNNs: Convolutional neural Networks
+
+![](media/final/ccn.PNG)
+
+## LSTMs: Long short term memory
+
+- Heavily used in natural language processing(NLP).
+
+![](media/final/lstm.PNG)
+
+# Probabilistic Learning (Ch. 20)
+
+## Maximum A Posteriori approximation (MAP)
+
+You assume the model which is most likely and use that to make your prediction.
+This is approximately equivalent to the Bayseian formula.
+
+Using the weighted average of the predictions of all the potential models, you make your prediction.
+
+
+``` python
+"""
+Equation 20.1
+    P(h_i|d) = gamma * p(d|h_i)p(h_i)
+gamma is 1/P(d) where P(d) is calculated by summing P(h_i|d)
+p(d|h_i) is simply the frequency of that bag in the wild times 
+the sum of the observations times their respective distribution
+in the bag.
+"""
+```
+
+## Maximum Likelihood approximation (MLE)
+
+This process has 3 steps: 1: write down expression for the likelihood of the data as a function of the parameters. 2: Write down the derivatives of the log likelihood with respect to each parameter. 3: Find the parameter values such that the derivatives are zero.
+
+
+## EM
+
+Used in k-means clustering.
+
+# Reinforcement learning (Ch. 21)
+
+MDP (Markov decision process): Goal is to find an optimal policy. 
+Often have to explore the space to learn the reward.
+
+
+## Bellman equation
+
+![](media/final/bellman.png)
+
+# Logic (Ch 7)
+
+- knowledge base  = set of sentences in a formal language
+- inference engine: domain-independent algorithms
+
+- declarative approach to logic: tell the agent what it needs to know
+
+![](media/final/propositional.png)
+
+- Logics are formal languages for representing information to make conclusions
+- syntax defines the sentences in the language
+- semantics define the meaning
+
+- A model are formally structured worlds with respect to which truth can be evaluated.
+
+## Propositional Logic
+
+- Assumes world contains facts: models evaluate truth values for propositional symbols. 
+
+![](media/final/propLogic.png)
+
+## Entailment
+
+- Entailment means that one thing follows from another. 
+- KB |= alpha. Knowledge base KB entails sentence "alpha" iff "alpha" is true in all words where KB is true. Ex: x + y = 4 entails 4 = x + y
+- AKA: entailment is a relationship between syntax that is based on meaning
+
+![](media/final/wumpus.png)
+
+## Inference
+
+- Inference: Deriving sentences from other sentences
+- Soundess: derivations produce only entailed sentences
+-Completeness: derivations can produce all entailed sentences
+
+
+## Forward chaining
+
+Forward chaining will find everything that is true in the logic. As a basic idea, this algorithm checks all rules that are satisfied in the knowledge base and add its conclusion to the knowledge base until the query is found. 
+
+## Resolution
+
+Resolution is sound and complete for propositional logic.
+
+
+## First-order logic (Ch #8)
+
+First-order logic (FOL) like natural languages assumes the world contains objects, relations, functions. Has increased expressiveness power over propositional logic.