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19 results for “decision”

Formulae (19)

Shannon Entropy

H = -\sum_{i=1}^{n} p_i \log_2 p_i

Measures the uncertainty or information content of a distribution.

Data Science & MLIntermediate

Gini Impurity

Gini = 1 - \sum_{i=1}^{n} p_i^2

Probability of misclassifying a random element; used in decision trees.

Machine Learning & AIIntermediate

Entropy (Information)

H(S) = -\sum_i p_i \log_2 p_i

Measures impurity/uncertainty of a set; used to split decision trees.

Machine Learning & AIIntermediate

Gini Impurity

G = 1 - \sum_i p_i^2

Probability of misclassifying a random sample; the default split metric in CART trees.

Machine Learning & AIIntermediate

Information Gain

IG = H(S) - \sum_k \dfrac{|S_k|}{|S|}H(S_k)

Reduction in entropy achieved by splitting a node on a feature.

Game Theory & DecisionBasic

Expected Value

EV = \sum_i p_i x_i

Probability-weighted average outcome of a decision.

Game Theory & DecisionAdvanced

Kelly Criterion

f^* = \frac{bp - q}{b}

Optimal fraction of bankroll to bet for long-run growth.

Game Theory & DecisionAdvanced

Expected Utility

EU = \sum_i p_i u(x_i)

Weighted average of the utility of outcomes, not just their cash value.

Game Theory & DecisionIntermediate

Payoff Comparison

a \succ b \iff u(a) > u(b)

One strategy dominates another if its payoff is always higher.

Game Theory & DecisionAdvanced

Minimax Value

v = \max_a \min_b u(a,b)

Best worst-case payoff a player can guarantee.

Game Theory & DecisionAdvanced

Mixed Strategy (Indifference)

p = \frac{d - c}{(a-b)+(d-c)}

Probability that makes an opponent indifferent between their options.

Game Theory & DecisionAdvanced

Bayes' Theorem

P(A|B) = \frac{P(B|A)P(A)}{P(B)}

Update a belief's probability given new evidence.

Game Theory & DecisionAdvanced

Value of Perfect Information

VPI = EV_{info} - EV_{no\,info}

How much better decisions become with full information.

Game Theory & DecisionIntermediate

Regret

R = u^* - u

Difference between the best possible payoff and the one you got.

Game Theory & DecisionBasic

Odds to Probability

p = \frac{o}{1 + o}

Convert betting odds into an implied probability.

Game Theory & DecisionIntermediate

Expected Payoff vs Mixed Opponent

E = \sum_j q_j u(a, b_j)

Your payoff when the opponent mixes strategies.

Game Theory & DecisionAdvanced

St. Petersburg Expected Value

EV = \sum_{k=1}^{\infty} \tfrac{1}{2^k} 2^{k-1}

A game with infinite expected value yet little real worth.

Game Theory & DecisionAdvanced

Shapley Value (2-player)

\phi_i = \tfrac{1}{2}(v(i) + [v(N) - v(j)])

Fair share of the total from a player's marginal contributions.

Game Theory & DecisionBasic

Break-Even Probability

p = \frac{L}{L + W}

Win probability needed for a bet to break even.