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39 results for “data”

Formulae (39)

Arithmetic Mean

\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i

The average of a data set.

Statistics & ProbabilityBasic

Median

M = \text{middle value of ordered data}

The middle value separating the higher and lower halves.

Statistics & ProbabilityBasic

Mode

\text{Mode} = \text{most frequent value}

The value that appears most often in a data set.

Statistics & ProbabilityIntermediate

Interquartile Range

IQR = Q_3 - Q_1

The spread of the middle 50% of the data.

Statistics & ProbabilityIntermediate

Interquartile Range

IQR = Q_3 - Q_1

Spread of the middle 50% of the data.

Statistics & ProbabilityBasic

Mode

\text{most frequent value}

The value that appears most often in a data set.

Data Science & MLBasic

Mean Squared Error (MSE)

MSE = \frac{1}{n}\sum_{i=1}^{n}(y_i - \hat{y}_i)^2

Average of squared differences between predicted and actual values.

Data Science & MLBasic

Root Mean Squared Error (RMSE)

RMSE = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_i - \hat{y}_i)^2}

Square root of MSE, in the same units as the target variable.

Data Science & MLBasic

Mean Absolute Error (MAE)

MAE = \frac{1}{n}\sum_{i=1}^{n}|y_i - \hat{y}_i|

Average of absolute differences between predictions and actual values.

Data Science & MLIntermediate

Coefficient of Determination (R²)

R^2 = 1 - \frac{\sum(y_i-\hat{y}_i)^2}{\sum(y_i-\bar{y})^2}

Proportion of variance in the target explained by the model.

Data Science & MLBasic

Classification Accuracy

Accuracy = \frac{TP + TN}{TP + TN + FP + FN}

Fraction of predictions that are correct.

Data Science & MLIntermediate

Precision

Precision = \frac{TP}{TP + FP}

Of all positive predictions, the fraction that were correct.

Data Science & MLIntermediate

Recall (Sensitivity)

Recall = \frac{TP}{TP + FN}

Of all actual positives, the fraction correctly identified.

Data Science & MLIntermediate

F1 Score

F_1 = 2\cdot\frac{Precision \cdot Recall}{Precision + Recall}

Harmonic mean of precision and recall.

Data Science & MLIntermediate

Specificity

Specificity = \frac{TN}{TN + FP}

Of all actual negatives, the fraction correctly identified.

Data Science & MLIntermediate

Sigmoid Function

\sigma(x) = \frac{1}{1 + e^{-x}}

Maps any real number to the range (0, 1); used in logistic regression.

Data Science & MLAdvanced

Softmax Function

\sigma(z_i) = \frac{e^{z_i}}{\sum_{j=1}^{K} e^{z_j}}

Converts a vector of scores into a probability distribution.

Data Science & MLBasic

ReLU Activation

f(x) = \max(0, x)

Rectified Linear Unit: outputs the input if positive, else zero.

Data Science & MLAdvanced

Binary Cross-Entropy Loss

L = -\frac{1}{n}\sum[y\log(\hat{y}) + (1-y)\log(1-\hat{y})]

Loss function for binary classification.

Data Science & MLAdvanced

Gradient Descent Update

\theta = \theta - \alpha \nabla J(\theta)

Iterative optimization step to minimize a cost function.

Data Science & MLIntermediate

Cosine Similarity

\cos\theta = \frac{A \cdot B}{\|A\|\|B\|}

Measures similarity between two vectors by the angle between them.

Data Science & MLBasic

Euclidean Distance

d = \sqrt{\sum_{i=1}^{n}(a_i - b_i)^2}

Straight-line distance between two points in n-dimensional space.

Data Science & MLBasic

Manhattan Distance

d = \sum_{i=1}^{n}|a_i - b_i|

Distance measured along axes at right angles (taxicab geometry).

Data Science & MLAdvanced

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.

Data Science & MLBasic

Z-Score Normalization

z = \frac{x - \mu}{\sigma}

Standardizes features to zero mean and unit variance.

Data Science & MLBasic

Min-Max Normalization

x' = \frac{x - x_{min}}{x_{max} - x_{min}}

Rescales features to the range [0, 1].

Data Science & MLAdvanced

Bias-Variance Decomposition

Error = Bias^2 + Variance + \sigma^2

Total expected error decomposes into bias, variance, and irreducible noise.

Data Science & MLAdvanced

Categorical Cross-Entropy

L = -\sum_{i=1}^{K} y_i \log(\hat{y}_i)

Loss for multi-class classification with one-hot labels.

Data Science & MLIntermediate

TF-IDF Weight

w_{t,d} = tf_{t,d} \times \log\frac{N}{df_t}

Term importance: frequency in a document scaled by rarity across documents.

Electronics & CircuitsAdvanced

Nyquist Bit Rate

C = 2B\log_2 M

Maximum data rate of a noiseless channel.

Unit ConversionsBasic

Gigabytes to Megabytes

\text{MB} = \text{GB} \times 1024

Convert gigabytes to megabytes (binary).

Unit ConversionsBasic

Bytes to Bits

bits = bytes \times 8

Convert bytes to bits.

Computer ScienceIntermediate

Nodes in a Full Binary Tree

N = 2^{h+1} - 1

Total nodes in a perfect binary tree of height h.

Computer ScienceBasic

Data Transfer Time

t = \frac{S}{R}

Time to transfer data of a given size at a rate.

Computer ScienceIntermediate

Parity Bit

p = b_1 \oplus b_2 \oplus \cdots \oplus b_n

XOR of data bits used for error detection.

Computer ScienceAdvanced

Nyquist Data Rate

C = 2B\log_2 L

Maximum data rate of a noiseless channel.

Computer ScienceAdvanced

Shannon Channel Capacity

C = B\log_2(1 + SNR)

Maximum error-free data rate of a noisy channel.

Computer ScienceAdvanced

Hamming Code Bits

2^r \geq m + r + 1

Parity bits r needed to protect m data bits.