EM Examples

EM Examples.carbide.md

EM Examples

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cell0.js

const jsonString = '{ name: Bob, children: { son: { name: MiniBob }, daughter: { name: Clara } }, age: fourteen }';

// function stringToJSON (str) {
//     const pairs = [];
    
//     for (const c in str) {
//         if (c === '{') {
//             // When you see a {, start a new array of pairs
            
//         }
//     }
// }

function leafString (str) {
    const pairs = [];
    let currentToken = '';
    let currentKey = '';
    
    for (const c of str.substring(1)) {
        // If it's a colon, save the current token as a key
        if (c === ':') {
            currentKey = currentToken;
            currentToken = '';
        }
        // If it's the end of a key, save the current (key, token) pair
        else if (c === ',' || c === '}') {
            pairs.push([ currentKey, currentToken ]);
            currentKey = '';
            currentToken = '';
        }
        else {
            currentToken += c;
        }
    }
    
    return pairs;
}



leafString('{ a: apple, b: boy, c: cat }');

// stringToJSON(jsonString);

cell1.js

function bracketParser (str) {
    const stack = [];
    const tokens = [];
    const results = [];
    let currentToken = '';
    
    for (const c of str) {
        if (c === '[') {
            stack.push(c);
            tokens.push(currentToken);
            currentToken = '';
        } else if (c === ']') {
            const left = stack.pop();
            if (currentToken.length) {
                results.push(currentToken);
            }
            currentToken = tokens.pop();
        } else {
            currentToken += c;
        }
    }
    
    return results;
}

bracketParser('[xxx[y[zzz]y]x]');

grades.js

const X = {"h":20,"c":10,"d":10}; ///_**X**_ is our **observable data**. In this case, it represents the **distribution of scores**, where\\- _h_ is the number of "A" and "B" grades//- _c_ is the number of "C" grades//- _d_ is the number of "D" grades\\In this example, _**X**_ is a proper subset of the "complete dataset" because we don't know the breakdown of "A" and "B" grades.

const { h, c, d } = X;  // destructuring for convenience




let mu = 0; ///_μ_ is the **parameter underlying our model**. In this case, it governs the distribution of **grades** as follows:\\- P("A") = 0.5//- P("B") = _μ_//- P("C") = 2_μ_//- P("D") = 0.5 - 3_μ_


let b; ///_b_ is the **sufficient statistic **whose expectation we are computing. In this case, _b_ denotes the **number of students who received "B" grades**; note that knowing _b_ fully determines the rest of the data set.
const numberOfIterations = 10; ///We fix a **number of times to perform EM**. As this value grows large, the MLE of the model parameters will converge.

const iterations = [];  // for logging

for (let t = 0; t < numberOfIterations; t += 1) {
    // E-Step: given mu, compute expectation of b
    b = (mu * h) / (0.5 + mu); ///**E-step: **given our current estimate for _μ_, compute 

    // Log for output
    iterations.push({ t, b, mu });

    // M-Step: use the b obtained in the E-Step to compute MLE for mu
    // P(X, z | theta) wrt theta
    mu = (b + c) / (6 * (b + c + d));
}

const finalMu = mu;

// GridArrayWidget
iterations;