Markov Decision processes

Markov decision process.PNG

A tuple – (S,s1,A,P,R)

S – finite set of states.

s1 – initial state.

A – finite set of actions.

P – Given a state s1 and action a, what is the probability of ending up at a particular state s2? This information is provided by P. This is called a State transition probability matrix. S*A*S

R – What is the reward for taking an action a at the state s?

Pi – Policy, what action to take at which state? A mapping from state space to action space. The optimal policy is the policy with the maximum reward.

Value function – Expected reward starting from state s and following policy pi.

Bellman equations –

Bellman

Ways to find an optimal policy:

Optimal policy when starting in state s is the policy whose value function is maximum starting from state s.

Think about the case where a particular policy is always better than another policy for all initial states. Then first policy is greater than second policy and this is called partial ordering.

Theorem:

There always exists a policy such that the partial ordering of it with all other policies is greater or equal. Such a policy/policies is called optimal policy.

Iterative methods:

  1. Policy iteration:
    1. At each state, pick the action with max value function.
    2. you get the new policy.
    3. Again go to step 1 and loop until the new policy and old policy are same.
  2. Value iteration:
    1. Finding an optimal value function rather than explicit policy.
    2. For every iteration improve value vector.
    3. once you converge to a particular value vector, use it to find the optimal policy.

Model-free methods:

Reinforcement learning is Markov decision process with unknown transition model and/or reward distribution.

Agent can observe samples and induce transition model and reward distribution from that.

Q-learning:

Uses Q-values instead of the value function.

To be continued……….


Credit assignment problem:

Advertisements

Decision trees

What are decision trees?

Decision trees are classification models built using a tree where a particular feature is selected for branching at different levels down the tree.

They help you to create non-linear boundaries with series of linear questions.

Decision tree

The primary choice to make is which feature to use for splitting first?

The objective in choosing the order of split is to further narrow down the possibilities faster. For example, Animal? Person? famous? living? singer? female? Michael jackson?

If you have started with Michael, if I said yes, then that’s good, but if I said no, you effectively narrowed down almost nothing.

We use info gain or Gini to make that decision.

Info gain:

infogain

but what does the info gain represent?

Info gain of a particular feature(work experience in above example) represents the predictability gain as we go down one level using that feature.

So, How is this predictability gain calculated?

This is measured by difference in predictability at parent node and expected sum of predictabilities in child nodes.

What is predictability at a node?

If number of positive and negative examples at a particular node is almost equal, then it is equally likely for a new example at that node to be either positive or negative.

If number of positive examples is far more than the number of negative examples at a particular node, then we can say with much more confidence that a new example at this node is more likely to be positive.

Second case is more predictable and contains less surprise, whereas first case is less predictable and has more surprise.

Now we use Entropy to quantify surprise at any node. How?

entropy

If all the samples belong to the same class, entropy is 0. If the samples are evenly distributed among all classes, then the entropy is 1.

  1. How to train?
    1. How to select the next best feature for branching?
      1. Calculate info-gain for all the features and select the one with maximum.
  2. How to predict?
    1. Just pass the test example down the tree and you have your classification at the leaf node.
  3. How to write a decision tree in python using scikit?
    1. writing the classifierdtclf
    2. visualizing the decision treevizdt

When to use decision trees?

  1. well-suited for categorical data.

How much training data do you need?

Nature of decision boundary

Decision trees are interpretable, unlike neural networks. Here you can exactly understand why a classifier makes a decision.

They are weak learners and hence good for ensemble methods.

They can handle unbalanced data sets, 1 % positive examples and 99 % negative examples.

This is Univariate – does not combine features.


Expressiveness among all possible decision trees in n-attributes:


How to deal with continuous attributes? Age,weight,distance

It does make sense to repeat an attribute along a path of a tree if attributes are discrete. If attributes are continuous, then you ask different questions for same attributes.


What to do to avoid overfitting in decision tree?

  1. like usually, using cross validation.
  2. Checking with cross validation at every time you expand the tree and the cv score is less than a particular threshold, then stop the expansion.
  3. Or first, expand the whole tree and start pruning back the leaves and check cv score at each step.

Algorithms:

ID3: Top down


Tuning parameters in sklearn:

  1. min_samples_split(default=2):  If node contains only n samples, then it will not be split any further.
  2. criterion=gini,entropy

Decision trees are generally prone to overfitting.

You can build bigger classifiers like ensemble methods using decision trees.

 

 

Glossary:

References:

https://www.analyticsvidhya.com/blog/2016/04/complete-tutorial-tree-based-modeling-scratch-in-python/#one

https://zyxo.wordpress.com/2010/09/17/why-decision-trees-is-the-best-data-mining-algorithm/

Computational combinatorics vs heuristics

In most of the AI algorithms, it is often the case that you enumerate in some sort and search through all the possible states and check whether we are at the goal state or particular constraints are being satisfied for the different combinations of states. This pretty much looks like a brute force and doesn’t seem to be intelligent though it could solve a pretty huge number of problems because of computational power we are endowed with. There would be a hard upper bound to the kind of problems we can tackle because of the computational limitation.

To make the search more efficient and more directional, we try to use human thought up heuristics into the search algorithms to guide the search. This is the crucial part of Human-machine interaction, leveraging the benefits of computational power and accuracy to the uniquely human-like heuristic intuition.

But the main question is, could we ever be able to make a computer think up its own heuristics appropriate to problem domain to guide its search?

Another question, How do we come up with heuristics in the first place? Do we develop it by copying the practices of our peers and mentors through our experience in the domain? or did we develop an innate sense of what to do when in some regular day to day chore settings because of millions of years of evolution? Is the ability to think up right heuristics is what true intelligence is?

Architecture for AGI

This article mainly runs on following dimensions.

  1. Perceiving the state of the world and state of yourself in the world.
    1. The power of discriminating and encapsulating different material and immaterial concepts which are often indefinitely defined, fuzzy, context -based and have no rigid boundaries.
      1. Natural language processing.
      2. Abstractions- clustering problem. Identifying the need for a level of clustering for current problem domain.importance of similarity measure in clustering. Rudimentary kind of clustering is clustering based on how different objects in the world be useful to him in what ways… Like things to eat to be clustered as one, things to talk to, things to use as the tool, or which body part to be used for what object. K-means algorithm.naive Bayes inferring classes from the models and models from the classes.em algorithm.
    2. pattern recognition.
    3. proprioception and self-referential systems.
    4. object recognition (https://www.youtube.com/watch?v=5yeusVF42K4)
    5. Donald Hoffman’s theory of perception.perceptual systems tuned to fitness outcompete those that are tuned to truth/reality.
  2. Goals and priorities in them.
    1. Switching between the goals based on the timeframes and dependencies for each goal.
    2. Inbuilt goals like getting sex, food, staying alive and goals we choose for ourselves by the culture and experiences and interaction between two kinds. Ethical issues of giving a power of creating self-goals to AI systems.
    3. Decision-making.
  3. Relevance measure for objects perceived in the world to the current goal.
    1. Prioritising perception or attention based on relevance to goal.
    2. Adaptivity of attention based on the skill level(acquired by repetition of the same process)
  4. Identifying actions or a sequence of actions to impact objects for achieving our goals.(planning)
    1. The element of stochasticity or randomness in finding the sequence is necessary to be creative when the sequence is unknown or not obvious.
    2. This can happen from analogies, empathy and copying, pattern recognition.
    3. Considering optimisation in face of multiple paths to a goal.
    4. related to imagination.
  5. A parallel Emotion machine with continuous feedback of utility or happiness on your present state in the world.
    1. Decision-making.
    2. operant conditioning.
  6. Platform knowledge: what information do we have at our birth about the world we are surrounded by and how to build it for a machine?
    1. Evolution.
    2. Jealous baby.
    3. A young baby doesn’t get surprised if a teddy bear passes behind a screen and reemerges as an aeroplane, but a one-year-old does.
    4. No categorical classification at the very beginning.
    5. As a child grows, a number of neurones decreases but a number of synapses increases.
  7. Knowledge representation, search and weights for retention(what you don’t use, you lose)
    1. Brain plasticity.
    2. Repetition and skill.
    3. Priming and classical conditioning.
    4. The DRM effect
    5. Do elements containing similar structure trigger each other.(Hofstader’s Danny in the grand canyon), pattern recognition by analogy.
    6. Reconstruction of data as memory at hippocampus with already existing memory.
    7. Procedural , episodic, semantic
    8. Representation of ideas that could be independent of language, which could allow for generalized reasoning to draw conclusions from combining ideas.
  8. Imagination at the core of knowledge, emotion machine and goals.
    1. Demis hassabis research on Imagination and memory.

What this article doesn’t talk about is:

  1. Whether a machine can have qualia even though it acts like it has general intelligence.Mary’s room. How to test qualia for a machine? Is Turing test enough for that?
  2. When did the consciousness first evolved and How?
  3. Moral implications of AGI and singularity.

Organising the interaction of all the above:

Why do I think I am talking about AGI? because we should be able to deduce any human endeavour from the interactions of above dimensions, at least from the infinitely long interactions and their orderings. Connections missed in below diagram:

  1. Goals to emotion machine.

my-agi-architecture

Deep dive (one at a time):

    1. Why object recognition is difficult?
      1. Objects defined based on purpose rather than its look or structure. We need to co-ordinate with module 3 and 7 to overcome this.
      2. We need to identify the object even though the viewpoint of it changes. When viewpoint changes, we have this problem of dimension hopping in training neural networks to recognize the object.Usually, inputs of neural networks for image recognition would be pixels, but when viewpoint changes, the input at one pixel at one training instance will be same at another pixel during different training instance. This is dimension hopping.#viewpoint_invariance.
    2. True language understanding is impossible without internal modeling the world.
  1.  Goals and priorities
  2. Relevance
  3. Planning (identifying action sequences):
  4. Emotion machine and utility:
  5. Platform knowledge: Jean Piaget, a child development psychologist argued that children create a mental model of the world around them and continuously modify that model as they interact with reality and receives feedback. He called this phenomenon as Equilibration.
    1. Infant reflexes .
    2. A child brain is less focussed with more learning rate on multitude of things, whereas an adult is more focussed, having better self control but with less learning rate.
    3. It seems true that humans come into the world with some innate abilities. some examples by steven pinker,
      1. when a human and a pet are both exposed to speech, human acquires the language whereas pet doesn’t, presumably because of some innate difference between them.
      2. Sexual preferences of men and women vary.
      3. Experimental studies on identical twins who are separated at birth and examined at later stages of life showing astonishing similarities.
      4. Do we have moral sense at birth?
    4. The above discusses about some facts on human nature at birth, but our main focus is to find Is there a seed meta-program that we are endowed with at birth which makes all other learning and behavior possible? If there exists what is it? These kinds of systems are called constructivist systems (thorisson).

Existing Cognitive Architectures: Two types

  1. Uniformity first:
    1. Soar Architecture
  2. Diversity first:
    1. ACT-R : intelligent tutoring systems are its application. John Anderson.

      Autocatalytic Endogenous Reflective Architecture (AERA)

Sigma architecture:

Architecture-requisite

Deep mind(Demis hassabis):

Deep learning + Reinforcement learning

Miscellaneous:

  1. Art is partly skill and partly stochastic.
  2. Poetry at the intersection of analogy and utility.
  3. How much of General and/or human intelligence has to do with reason? If it is fully correlated with reason and morality is built on only reason, then we and AGI has no conflict of interest as more intelligence only means more morality. #moralitynintelligence
  4. Value system guiding attention, attention setting the problem domain, problem domain looking for heuristics, heuristics guiding the search path.

Glossary:

  1. Distributed representation: Many neurones are involved in representing one concept and one neurone is involved in representing many concepts.

Artificial Intelligence

Definition: The study and design of intelligent agents, where an intelligent agent is a system that perceives its environment and takes actions that maximize its chances of success.


Agent and environment:

Rational agent: The agent which selects the action that maximizes its performance measure given its inputs or perceptions and built-in knowledge.

PEAS: Performance, Environment, Actuators and Sensors

Types of Environment:

  1. Fully vs partially observable:
  2. Deterministic( vs stochastic): The next state of the environment is completely determined by the current state.
  3. Episodic vs sequential: Each perception-action pair can be considered as an episode.
  4. static vs dynamic:
  5. discrete vs continuous:
  6. single-agent vs multi-agent:
  7. known vs unknown:

Types of Agents in the order of increasing generality:

  1. Simple reflex agents: based on current state only. Look up the table of percepts and actions.
  2. Model-based reflex agents: based on percept history, maintains a model of the world, condition-action rules decide the action of the agent.
  3. Goal-based agents: contains goal information additional to Model-based agents.Goals decide the actions of the agent.
  4. Utility-based agents:  Utility function is the agent’s performance measure. try to increase the happiness.
  5. Learning agents:

Agent’s organisation:

  1. Atomic representation: Consider each state as a black box.
  2. Factored representation: Each state has attribute value properties.
  3. Structured representation: Relationship between objects inside a state.

Search Agents

General example problems from AI textbook:

  1. Travelling salesman problem.
  2. Route finding problem
  3. Robot navigation
  4. protein design

State space, search space and search tree.

Measures:

  1. Completeness: Can the algorithm find a solution when there exists one?
  2. Optimality: Can the algorithm find the least cost path to the solution?
  3. Time complexity: How long does it take to complete the search.
  4. Space complexity: How much memory is needed to complete the search.

Compare search

Two types of search:

  1. Uninformed: No information about the domain.
    1. Breadth-first: FIFO
      1. bfs
      2. Applications: computing shortest path when all the edge lengths are same.
    2. Depth first: LIFO
      1. dfs
      2. Depth limited is not optimal because it might return us a high-cost path on the left sub-tree without considering other low-cost paths in the right subtree.
      3. Applications: Topological ordering of directed acyclic graphs.
    3. Depth limited: Depth first with depth limit
    4. Iterative deepening: Depth limited with increasing limit, combines benefits of depth first and breadth first. First do depth first search to a depth limit n and then increase the depth and do depth first search again. diff of BFS and IDS
    5. Uniform cost: Expand least cost node first, FIFO
      1. Dijkstra’s algorithm is a variant of ucs, except that ucs finds shortest path from start node to goal node, whereas Dijkstra finds shortest path from start node to every other node.ucs and Djikshtra.Computing shortest path when edge lengths are different. Use heap data structure for speed.
      2. I doubt Google uses UCS for it’s route finding in maps. Cost between the nodes can be a mix of distance, traffic, weather etc.Maps algorithm
        1. ucs
  2. Informed: Some information about the domain and goals.
    1. Heuristics search (h(n)): Determine how close we are to the goal based on a heuristic function. Admissible heuristic thinks that the cost to the solution is less than the actual cost.
      1. Greedy search expands the node that appears to be closest to the goal. uses a heuristic function that has the information of cost from a particular node to the target node.
        1. greedy search.PNG
      2. A* search:  Consider both the heuristic that says about the cost from a node to the target node and cost to reach that node. A* search will revise it’s decision, whereas greedy search would not. This property makes greedy incomplete and A* complete.
      3. IDA*:
  3. Local search: iterative improvement algorithms by an optimization/fitness function.
    1. Hill climbing (steepest descent/ascent,greedy local search):some variants of this are:hill-climbing
      1. sideways moves – escape flat lines.
      2. Random restart – to overcome local maxima.
      3. Stochastic –
    2. Simulated annealing : from statistical physics.
    3. Local beam search – k states instead of single state.
    4. Genetic algorithms: from evolutionary biology
      1. genetic algo.PNG

Adversarial search and games:

Multiagent environment, uncontrollable opponent.

Not a sequence of actions, but a strategy or policy.

Approximation is the key ingredient in the face of combinatorial explosion.

Types of games.PNG

(perfect information, deterministic) – Zero sum games.

At any stage, one agent will try to pick the move with maximum utility out of all legal moves and the opponent will pick the move with minimum utility.

Embedded thinking or backward reasoning:

Thinking through the consequences and potential actions of the opponent before making the decision.

Minimax : Two opponents playing optimally, one trying to maximize and other trying to minimize the utility.

Alpha-Beta pruning:

When the agent that is trying to find Max utility of it’s children, you start with an alpha as (-infinity), and update alpha if you find any child nodes with utility better than present alpha. During this process, if you come across any 2nd gen childs with utility less than alpha, then you don’t need look for utilities of other 2nd gen childs of that particular 1st child. Why? because that 1st gen child is trying to find minimum, once you go down below alpha, that 1st gen child is out context at the zeroth generation which is trying to find max has found that this 1st gen child can no longer contribute to me. In this context, ordering of child nodes matters a lot. Right ordering can save you from exploring lot of unnecessary childs/paths.

Stochastic/Non-deterministic games:

A chance/random element involved.

Expectiminimax.

Machine Learning:

Data collection -> Data preparation -> Exploratory Data analysis(picture the data using different graphs and charts) -> Machine learning techniques -> Visualization -> Decision

  1. Decision trees:
  2. Rule induction:
  3. Neural networks:
  4. SVMs
  5. Clustering method
    1. K-means
    2. Gaussian mixtures
    3. Hierarchical clustering
    4. Spectral clustering.
  6. Association rules
  7. Feature selection
  8. Visualization
  9. Graphical models
  10. Genetic algorithm

Statistics:

  1. Hypothesis testing
  2. Experimental design
  3. Anova
  4. Linear regression
  5. Logistic regression:
    1. It is a linear classifier, why?
      1. Because the decision boundary where the probability=0.5 is linear.
  6. GLM
  7. PCA

Definition of Machine learning:

A computer program is said to learn from experience E with respect to some class of tasks T and performance P, if its performance at tasks in T , as measured by P, improves with experience E.

BY it’s very definition, Machine learning algorithms are generally subdued to a particular class of tasks and not generic enough for general intelligence.

K-nearest neighbors:

O(n*d) – n is the number of training examples and d is the number of features.

K is usually chosen as odd value.

z-scaling – Each feature has a mean of 0 and a standard deviation of 1.

kernel regression is a flavour of k-nearest neighbors where we weight the contribution of each neighbor, where as in k-nearest neighbor we just take the average.

Applications:

Recommender systems (collaborative filtering).

Breast cancer diagnosis

Handwritten character classification

information retrieval


 

To Avoid over fitting:

Reduce number of features manually or do feature selection.

Do a model selection

Use regularization (keep the features but reduce their importance by setting small parameter values)

Do a cross validation to estimate the test error.

Training set used for learning the model.

Validation set is used to tune the parameters, usually to control overfitting.

Linear Models:

  1. Linear regression.
    1. Using least square loss
  2. Linear classification:
    1. Perceptron: Data has to be linearly separable.

Classification: Logistic regression

Decision Trees: Tree classifiers

Start with a set of all our examples at the top root node.

Create branches considering a splitting criteria and repeat this for creating other branches as you go down.

write the final decision at the bottom of the tree based on training examples and used this tree to classify any new test data.

First, we calculate entropy at a node and then compare info gains for extending that node for different dimensions. Then we choose to extend based on the category of high info gain.

Pruning strategies to escape overfitting:

  1. Stop growing the tree earlier.
  2. Grow a complex tree and then prune it back. Remove a subtree and check it against a validation set, if the performance doesn’t degrade, remove the subtree from original.

Cart method:

Another method to build a decision tree.

  1. Adopt same greedy, top-down algorithm.
  2. Binary splits instead of multiway splits.
  3. Uses Gini index instead of information entropy.

Gini=1-p^2-P^2

p-proportion of positive examples

P-proportion of negative examples.

Bayes Rule:

Bayes rule.PNG

Discriminative Algorithms:

Idea: Model p(y/x), conditional distribution of y given x.

Find a decision boundary that separates positive from negative example.

Generative Algorithms:

modelling for Bayes rule.PNG

Naive Bayes assumes that feature values are conditionally independent given the label.

Naive Bayes classifier is linear.

Naive Bayes.PNG

Ensemble Methods:

An Ensemble method combines the predictions of many individual classifiers by majority voting.

Such individual classifiers, called weak learners, are required to perform slightly better than random.

  1. Majority voting:
    1. Condorcet’s Jury theorem:
      1. Assumptions:
        1. Each individual makes the right choice with a probability p.
        2. The votes are independent.
      2. If p>0.5, then adding more voters increases the probability that the majority decision is correct. If p<0.5, then adding more voters makes things worse.
  2. Boosting:
    1. One of the most popular Machine learning methods.
    2. AdaBoost.M1-popular algorithm.
    3. Weak learners can be trees, perceptrons, decision stumps etc.
    4. The predictions of all weak learners are combined with a weighted majority voting.
    5. Idea: Train the weak learners on weighted training examples.AdaBoost.PNG
      1. AdaBoost with Decision stumps lead to a form of feature selection.
      2. Bootstrapping is a resampling technique for training weak learners from m samples of original training data.
    6. Iteratively give more weight on examples that are misclassified and less weight for examples that are classified properly.(Refer weight updation step d in above picture).
    7. Boosting.PNG
    8. Boosting tends to avoid overfitting because of increasing margin as you add more and more weak learners.
    9. Boosting tends to overfit if weak learners themselves are overfitting.
  3. Bagging:Bagging.PNG
    1. Bagging on trees works better than building a big tree on whole data.
  4. Random forests: Make a lot of decision trees with each tree trained on a random subset of training data and a random subset of all features considered. use the majority votes of different decision trees to determine the final outcome for a random forest. This is relying on the principle that majority of decision trees will compensate for some wrongly classifying decision trees at different instances.
    1. Quora uses random forests for determining whether two questions are duplicates.

A practical guide to applying Support Vector Classification:

Clustering examples:

  1. Clustering of the population by their demographics.
  2. Audio signal separation.
  3. Image segmentation.
  4. Clustering of geographic objects
  5. Clustering of stars.

Desirable clustering properties:

  1. Richness: For any assignment of objects to clusters, there is some distance matrix D such that a clustering scheme returns that clustering. For example, Stop when clusters are x units apart reached is rich because it can address all possible clusterings with variations of x. On the other hand, stop when a fixed number of clusters reached, is not rich because it can’t address all possible clusters.
  2. Scale invariance: Scaling distances by any value shouldn’t change the clustering of the objects.
  3. Consistency: Shrinking(making similar things more similar) intra cluster distances and expanding(making non-similar things more non-similar) inter clustering distances shouldn’t change the clustering.

Impossibility theorem: No clustering algorithm can achieve all three of richness, scale invariance, and consistency.

K-means:

  1. Based on initial conditions of the centroid, you may end up with totally different clusters. To deal with this, we take the ensemble of clusterings with different initializations. n_init parameter determines that.
  2. sklearn.cluster.KMeans(n_clusters=8,max_iter=300, n_init=10).

Limitations of k-means:

  1. Output for any given training set would always be same as long as we do not randomly pick initial centroids. But we usually choose centroids randomly in the beginning.
  2. Hill climbing algorithm.

K-means fails for:

 

Solution for How to select K.

G-means:G-Means betterment of k-means.PNG

How to evaluate?

internal evaluation: High intra-cluster similarity, Low inter-cluster similarity.

External evaluation: Mutual information, entropy, adjusted random index.

Other clustering methods:

  1. Special clustering
  2. DBSCAN
  3. BIRCH

1.Single linkage clustering:

Keep on finding two closest points among all points and join them as long as you end up with k required clusters. This is a hierarchical agglomerative cluster structure.

single linkage cluster.PNG

Association Rules:

Supp(A->C): P(A^C)

Probabilistic interpretation:

R: A->C

conf(A->C)=P(C/A)=P(A^C)/P(A)

Though this looks like a valid measure, it doesn’t take into account P(C).

Interest(A->C)=P(A^C)/(P(A)*P(C))=Conf(A->C)/supp(C)

interest(R)=1 then A and C are independent.

interest(R)>1 then A and C are positively dependent.

interest(R)

Applications:

Collaborative filtering, customer behavior analysis, web organization, affinity promotion, cross-selling

Multidimensional rules:

Read more about Quantitative Association rules as well.

CONSTRAINT SATISFACTION PROBLEMS:

Care about goal rather than the path.

intelligence_levels

Three elements:

  1. A set of variables.
  2. A set of domains for each variable.
  3. A set of constraints that specify allowable combinations of values.

Types of consistency:

  1. Node consistency – unary constraints
  2. Arc-consistency (Constraint propagation)- binary constraints – For every value that can be assigned to X, if there exists a value that can be assigned to Y, then X->Y is arc consistent. AC-3 is the algorithm that makes a CSP arc consistent. O(n^2*d^3)
  3. Path-consistency – n-ary constraints

Forward checking propagates the information from assigned to unassigned variables only and does not check the interaction between unassigned variables. Arc consistency checks for all arcs and keep doing it whenever the domain of a variable is reduced. In this sense, AC is more general and an improvement of FC.

Two types of CSPs:

  1. Search based
    1. BFS
    2. DFS
    3. BTS
  2. Inference

Choose the one with minimum remaining values to fill first.

Fill with least constraining value first – the one that rules out fewest values in remaining variables.

Can work on independent subproblems separately based on the problem structure.

Backtracking:

d-size of domain, n-number of variables.

O(d^n)

Reinforcement learning:

Learning behaviour or actions based on the rewards/feedback from environment.

Science of sequential decision making.

  1. Markov decision process – Formal model for sequential decision making.
    1. Markov property – Future is independent of the past given the current state.
    2. Applying reinforcement framework to Markov process.
    3. Theorem – Due to the Markov property, A discounted MDP always has the stationary optimal policy (pi).
    4. A policy is better than another policy if it’s value is greater than the other one calculated from all starting states.
    5. One useful fact is there always exist an optimal policy which is better than all other policies.
    6. Bellman equations.
    7. No closed form solution to Bellman equations to solve for optimal policy.
    8. other iterative solution approaches are
      1. Policy iteration.
      2. Value iteration.
    9. Think of different policies to traverse through MDP. Calculate value of each policy.
    10. Q-value iteration.
    11. Epsilon greedy exploration – with probability epsilon, take random action, with probability (1-epsilon) , take greedy action.

Logical agents or knowledge-based agents:

Mainly based on knowledge representation(domain specific) and inference(domain independent).

  1. Using propositional logic.
  2. Using First – Order Logic – used in personalized assistants.

pros and cons of Logical agents:

  1. Doesn’t handle uncertainty, probability does.
  2. Rule-based doesn’t use data, ML does.
  3. It is hard to model every aspect of the world.
  4. Models are encoded explicitly.

Resolution algorithm

Natural Language Processing:

Text classification (spam filtering)- Naive Bayes classifier.

Sentiment analysis

Naive bayes classifier – Assumes features are independent.

Classifies the new example based on the probabilities of different classes given the features of that particular example.

m-estimate of the probability:

  1. Augment the sample size by m virtual examples, distributed according to prior p.

Chain rule of probability:

  1. To estimate joint probability

N-gram model: Look N-1 words in the past to predict next word.

Bigrams capture synctactic dependencies such as noun comes after eat and verb comes after to etc.

3-grams and 4-grams are common in practice.

Perplexity – Hiigher the conditional probability, lower the perplexity.

Great progress:

Tagged text – which word is what type – noun, adjective,verb

Name entity recognition – yesterday(time), I(person), five (quantity)

Good progress:

Parsing – Exhibit the grammatical structure of a sentence.

Sentiment analysis – Does it identify sarcasm?

Machine translation

Information extraction.

work in progress:

Text summarization

Question/Answering

Dialog systems: Siri, echo etc.


Deep learning :

  1. Less or no feature engineering required.
  2. Need to choose number of layers in the stack and number of nodes in each layer.
  3. Needs to be sensitive to minute details to distinguish between two breeds of a dog and at the same time, it should be invariant to large irrevelant variations like background, lighting and pose etc.
  4. ReLU usually learns much faster in networks with many layers compared to sigmoid.
  5. Pre-training was only needed for small data sets with the revival of deep learning.
  6. Convnet combined with recurrent net to generate image captions. Vision to language interface.
  7. Handwritten characters, spoken words, faces were most succesfull applications.
  8. Theorem: No more than 2 hidden layers can represent any arbitrary region (assuming sufficient number of neurons or units).
  9. The number of neurons in each hidden layer are found by cross validation.
  10. The Mammalian visual cortex is hierarchical with 5-10 levels just for the visual system.
  11. Examples of Deep neural networks – Restricted Boltzmann machines, convolutional NN, autoencoders etc.
  12. Software for Deep learning:
    1. Tensorflow – Python
    2. Theano – Python
    3. Torch – LUA
    4. Caffe – Suited for vision

Robotics:

Path planning:

  1. Visibility graph: VGRAPH – A-star search through the nodes between obstacles. guaranteed to give shortest path in 2d. Doesn’t scale well to 3d. Path close to obstacles (nodes at vertices).
  2. Voronoi path planning:
  3. Potential field path planning: Consider both robot and obstacles as positive charges repelling each other and Goal as negative charge attracting the robot. Take a Random walk in case you reach a local minimum.
  4. Probabilistic roadmap planner: First needs to sample the space entirely and detect some collision free nodes. connect k nearest neighbor nodes. then do graph search to go from start to goal with these connected nodes. Can’t be sure that all nodes will be connected.

Glossary:

  • Discriminative models learn the (hard or soft) boundary between classes
  • Generative models model the distribution of individual class.
  • Confusion matrix.
  • ply – each move by one of the players.
  • policy – State to action mapping
  • stationary policy -Particular action for a particular state all the time.
  • Representation learning – automatically discovers representations required to classify or predict, Not much feature engineering required. Ex: Deep learning.
  • Saddle points/ minimax point – where derivative of the function is zero, but because of max in one ax and min in other axes. In the shape of the saddle on the horse.
  • Unsupervised pre-training – Making features before feeding into the learning network.
  • Configuration space(C – space): Set of parameters that completely describe the robot’s state. Proprioception.

CREDITS: Columbia University

Naive Bayes

Bayes theorem helps us to incorporate new evidences/information into our model.

Code from sklearn

from sklearn.naive_bayes import GaussianNB

clf=GaussianNB()

clf.fit(features_train,labels_train)

Bayesian Learning:

Bayesian learning.PNG


Naive bayes

 

Linear in the number of variables.

Naive Bayes assumes conditional independence across attributes and doesn’t capture inter-relationship among attributes.

Gaussian naive Bayes assumes continues values associated with each class are distributed in Gaussian fashion.

Even if the probability of one of the attributes given label becomes zero, the whole thing ends up being zero.

Machine learning

Pandas and numpy:

numpy.mean(df[ (df.gold>0) ][“bronze”])

olympic_medal_counts = {‘country_name’:countries,
‘gold’: Series(gold),
‘silver’: Series(silver),
‘bronze’: Series(bronze)}
df = DataFrame(olympic_medal_counts)

del df[‘country_name’]
# YOUR CODE HERE
avg_medal_count=df.apply(lambda x:numpy.mean(x))

b=numpy.array([4,2,1])

a=numpy.column_stack((numpy.array(gold),numpy.array(silver),numpy.array(bronze)))

points=numpy.dot(a,b)

olympic_points_df=DataFrame({‘country_name’:countries,’points’:points})

df[‘points’] = df[[‘gold’,’silver’,’bronze’]].dot([4, 2, 1]) olympic_points_df = df[[‘country_name’,’points’]]


Preprocessing:

For highly-skewed feature distributions such as 'capital-gain' and 'capital-loss', it is common practice to apply a logarithmic transformation on the data so that the very large and very small values do not negatively affect the performance of a learning algorithm. Using a logarithmic transformation significantly reduces the range of values caused by outliers. Care must be taken when applying this transformation however: The logarithm of 0 is undefined, so we must translate the values by a small amount above 0 to apply the the logarithm successfully.

Scaling:

In addition to performing transformations on features that are highly skewed, it is often good practice to perform some type of scaling on numerical features. Applying a scaling to the data does not change the shape of each feature’s distribution (such as 'capital-gain' or 'capital-loss' above); however, normalization ensures that each feature is treated equally when applying supervised learners. Note that once scaling is applied, observing the data in its raw form will no longer have the same original meaning, as exampled below.

We will use sklearn.preprocessing.MinMaxScaler for this.

If data is not normally distributed, especially if the mean and median vary significantly (indicating a large skew), it is most often appropriate to apply a non-linear scaling — particularly for financial data. One way to achieve this scaling is by using a Box-Cox test, which calculates the best power transformation of the data that reduces skewness. A simpler approach which can work in most cases would be applying the natural logarithm.

Identifying Outliers:

Tukey’s method


 

 

from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.25)

R2 score:

r2 score.PNG

If {\bar {y}} is the mean of the observed data:

{\bar {y}}={\frac {1}{n}}\sum _{i=1}^{n}y_{i}

then the variability of the data set can be measured using three sums of squares formulas:

SS_{\text{tot}}=\sum _{i}(y_{i}-{\bar {y}})^{2},
SS_{\text{reg}}=\sum _{i}(f_{i}-{\bar {y}})^{2},
{\displaystyle SS_{\text{res}}=\sum _{i}(y_{i}-f_{i})^{2}=\sum _{i}e_{i}^{2}\,}

The most general definition of the coefficient of determination is

R^{2}\equiv 1-{SS_{\rm {res}} \over SS_{\rm {tot}}}.\,

 

Accuracy = true positive + true negatives/total

from sklearn.metrics import accuracy_score

accuracy_score(y_true,y_pred)

Accuracy is not a right metric when data is skewed.


 

Precision:

precision.PNG

Recall:

Recall.PNG

 

f beta.PNG


ROC CURVE:


Errors:

Underfitting: Error due to bias, Oversimplified model, performs badly on both training and testing data.

Overfitting: Error due to variance. Over complicated model. model is too specific, performs badly on testing data.

Model complexity graph:

Model complexity graph.PNG

Training set: for training model.

Cross validation set: for choosing right parameters like degree of the polynomial. Useful to check whether the trained model is overfitting. If trained model performs poorly on this cross validation set, then the model is overfitted.

Testing set: For final testing.

K-FOLD CROSS VALIDATION:

Divide all your data into k buckets and iteratively create models by choosing one bucket as testing set and remaining for training.

Use average of these models for final model.

K-FOLD.PNG

 

If you increase training points on different models:

 

Grid Search CV:

GRID SEARCH CV.PNG


Plot learning curves to identify when to stop collecting data.


Supervised learning:

If there is an order in output data, then go for continuous model. Ex: income, age.

If there is no order, go for a discrete model. Ex: phone numbers, persons


Algorithms to minimize sum of squared errors:

  1. Ordinary least squares: sklearn LinearRegression.
  2. Gradient descent.

There can be multiple lines that minimize |error|, but only one that minimizes error^2.


Instance based learning:

Properties:

  1. Remembers.
  2. Fast and doesn’t learn.
  3. simple.
  4. No generalization.
  5. Sensitive to noise.

 

  1. Look up:

In k-nn all features matter equally because when we calculate distance, all features are treated equally.

 

Locally weighted regression (evolved from k-nearest neighbors):


Naive bayes:

Powerful tools for creating classifiers for incoming labeled data.


Expectation maximization:

expectation maximization.PNG

This is very similar to k-means clustering.

EM is for soft clustering when there is any ambiguity regarding which data point to move to which cluster.


Which supervised classifiers are suitable for numerical as well as categorical data?

The data you have is called ‘mixed data’ because it has both numerical and categorical values. And since you have class labels; therefore, it is a classification problem.  One option is to go with decision trees, which you already tried. Other possibilities are naive Bayes where you model numeric attributes by a Gaussian distribution or so. You can also employ a minimum distance or KNN based approach; however, the cost function must be able to handle data for both types together. If these approaches don’t work then try ensemble techniques. Try bagging with decision trees or else Random Forest that combines bagging and random subspace. With mixed data, choices are limited and you need to be cautious and creative with your choices.


Feature scaling:

To give equal importance to all the different features, we can normalize them to the range of 0 to 1 before applying learning algorithm.

x-x_min/(x_max-x_min)

from sklearn.preprocessing import MinMaxScaler

scaler=MinMaxScaler()

rescaled_weights=scaler.fit_transform(weights)

Feature rescaling would be useful in k-means clustering and rbf svm where we calculate distances but not much in decision trees and linear regression.


Feature selection:

why?

  1. Knowledge discovery, interpretability, and insight. To identify which features actually matter among all of them.
  2. Curse of dimensionality – The amount of data that you need to train grows exponential to the number of features that you have.

NP-HARD


Feature selection:

Filtering(fast) and Wrapping(slow):

knn suffers from curse of dimensionality because it doesn’t know which features are important. So, we can use decision trees as filtering mechanism to determine important features and then pass them on to knn for learning.

Wrapper methods evaluate subsets of variables which allows, unlike filter approaches, to detect the possible interactions between variables.


Relevance:

  1.  A feature is said to be strongly relevant if the Bayes optimal classifier’s performance is strongly affected by the absence of this feature.
  2. A feature is weakly relevant if there exists some other feature which can suffice the purpose of this feature.
  3. Depends on how much information a feature provides.

Usefulness:

  1. Depends on error/model/learner.

Composite feature:

composite feature.PNG


When to use PCA?

  1. When some latent features are driving the patterns in the data.
  2. Dimensionality reduction, reduce noise, better visualization.

Feature transformation:

Independent Component analysis: cocktail party problem.

PCA vs ICA.PNG

Other feature transformations:

  1. Random component analysis – Fast and it usually works.
  2. Linear discriminant analysis –

Design patterns

 

Design that is more automated and require less maintenance is the standard.

Getters and setters:

Setters can be used for validation and constraining the value to be set to a particular range.

Getters can be used for returning default value, if the variable is not set yet or for lazy instantiation.


Can’t make objects out of abstract class. Abstract class can have some non abstract members.

Interface have only abstract methods.


 

Image result for design patterns java


Creational:

  1. Singleton:
    1. Can only have one instance of that particular class.
    2. President of a country, System in java.
    3. Private constructor, singleton using enum.
    4. @Singleton annotation.
    5. Difficult to unit test – why?
  2. Factory:
    1. Having a logic to return a particular subclass object, when asked for a class object.
  3. Abstract Factory:
  4. Builder:
    1. Separates object construction from its representation.
    2. interfaces.
  5. Prototype:
    1. Chess game initial setup.
    2. Copying/cloning the initial setup rather than creating the initial setup everytime you need it. Reduce redundant work.
    3. Copy a fully initialized instance.
    4. Link to code.

How to create objects?

Structural:

Inheritance? Interface? etc.

How are different classes related?

How are objects composed?

  1. Adapter:
    1.  Match interfaces of different classes. helps to communicate.
  2. Composite:
  3. Proxy:
    1. An object representing another object, like credit card as a proxy of bank account.
    2. Remote object and Home object(proxy).
  4. Flyweight:
    1. Reuse same objects by resetting values of the objects appropriately instead of creating new objects every time.
  5. Facade:
    1. Event managers, process, execute, group many steps into a single step.
  6. Bridge:
  7. Decorator:
    1. Add responsibilities to objects dynamically.
    2. Ex: adding different Toppings for different pizzas, adding discounts to different orders.

Behavioral:

Interactions between different objects.

  1. Template method:
  2. Mediator:
    1. instead of applications talking to each other, we use an enterprise service bus.
  3. Chain of responsibility:
    1. Passing a request through different objects.
  4. Observer:
    1. A way of notifying a change to a number of classes.
    2. This pattern is implemented in java.
    3. Subject extends Observable.
    4. Who wants to listen implements Observer and registers with the subject.
  5. Strategy:
    1. change the implementation/strategy of an interface at a later point in time.
    2. Pass whatever implementation needs to be used as an argument.
  6. Command:
    1. Encapsulate a command request as an object.
    2. java.lang.runnable threads are implemented like this.
  7. State:
  8. Visitor:
    1. Adding new operations to a particular class without inheritance and wi
  9. Iterator:
    1. Sequentially access the elements of a collection.
  10. Interpreter:
  11. Memento:
    1. Saving states of something as objects to restore them in future point of time if necessary.
    2. Undo/Redo operations.

Strategy pattern:

What:

 

Strategy design pattern.PNG

When:

Strategy pattern - when.PNG


Observer pattern:

when:

Observer pattern - when

What:

Observer pattern

Factory pattern :

Factory pattern - whenFactory pattern

Abstract Factory pattern:

Singleton pattern:

Singleton pattern.PNG

 Builder pattern:

Builder pattern.PNG

Prototype pattern:

 

Dependency injection

dependency injection1.PNG

What is dependency injection?

Instead of initiating the object we are dependent on, we take help of a dependency framework which will push the ready made object to the dependent class during runtime.

In the above picture we are not initializing hotDrink with new hotDrink(), instead we are getting it as a constructor parameter.

Why is it useful?

This is useful to decouple two different code packages and remove direct dependency.

If you have an interface which can have multiple implementations, with the dependency injection framework, you can choose to run which implementation to run at runtime. Suppose you want to isolate and test a particular package, you can provide mock implementations of all other interfaces it is dependent on.

If you have to do the same without DI injection and interfaces, then you need to change code in lot of places, calling mock object at all the places you were calling original object to test.

It is useful when you have dependencies depending on other dependencies and so on.

Implementing with Google Guice:

Guice diGuice di2

You should usually initialize the injector where you bootstrap the program.

bind or guice configure() helps you define which implementation of interface to use.

@implementedby annotation can be used instead of configure() and bind.

@implementedby can be used as a default one.

If both guice module(bind) and @implementedby compete for different implementations of same interface, guice module wins.


 

Wanna have conditional logic to pick implementations?

Providers


Dependency injection without interface:

 

Dependency injection

Enable a class to be generic by making it disown the responsibility of defining an object in itself. Make other classes define the input object for it.

If you want to change the input object , you dont need to change the original class with dependency injection.

dependency injection

A spring container contains a set of objects or beans.

Essence of Rich Dad Poor Dad

Identify what are assets and what are liabilities.

Increase asset column.

Don’t work for money, make money work for you.

Rich buy luxuries late.

Rich guys income statement and balance sheet.

rdpd.jpg

How corporations help rich with taxes.

5oxAy.png

Corporations earn, spend and then pay taxes on the rest.

Individuals earn, get taxed and then spend.

Listing some assets:

  1. Businesses that do not require my presence.
  2. Stocks – Fortunes are made in new stock issues(new stocks are tax-free).
  3. Bonds.
  4. Income generating real estate.
  5. Notes (IOUs).
  6. Royalties from intellectual property.

Dimensions of financial literacy:

  1. Accounting:
  2. Investing:
  3. Understanding markets:
  4. The law: