In machine learning, an experiment refers to the process of training, validating, and testing a model under specific conditions, followed by analyzing and interpreting the results. A single experiment may include selecting a type of model, defining hyperparameters, pre-processing the data, training the model, and evaluating its performance.

Experiments in machine learning are iterative; the results of one experiment inform adjustments to the model or its parameters for the next experiment. The ultimate goal of these experiments is to find a model and set of parameters that perform optimally for the task at hand.

Here is a detailed walkthrough of a typical machine learning experiment:

Data Preprocessing: This is the first stage of the experiment, which involves preparing the data for machine learning. Depending on the dataset and the problem, this can include tasks like handling missing values, encoding categorical variables, scaling numerical variables, and so forth. For instance, missing numerical values might be filled in with the mean value of the available data, denoted as µ:
Xmissing = µ(X_available)

Model Selection: Choose a type of machine learning model appropriate for the task. For example, you might choose a linear regression model for a regression task or a convolutional neural network for an image classification task.

Hyperparameter Tuning: Define or tune hyperparameters for the model. Hyperparameters are parameters that are set before training and control aspects of the training process. For instance, the learning rate, denoted as α, is a common hyperparameter that controls how much the model changes in response to the estimated error each time the model weights are updated.

Model Training: Train the model on the training set of data. This involves inputting the training data to the model and adjusting the model's weights based on the computed loss. In the case of a simple linear regression model, this could be represented as:
y = β0 + β1X + ε
where y is the target variable, X is the input variable, β_0 and β_1 are the parameters to be learned (intercept and slope, respectively), and ε represents the error term.

The parameters are learned by minimizing a loss function, which quantifies how well the model's predictions match the true values. For example, a common loss function for regression tasks is the mean squared error (MSE):
MSE = 1/N Σ(y_true - y_pred)^2
where N is the number of samples, y_true are the true values, and y_pred are the predicted values.

Model Evaluation: Once the model has been trained, it's time to evaluate its performance on unseen data. This usually involves using a validation set during the training phase to tune hyperparameters and avoid overfitting, and a test set after training to provide an unbiased evaluation of the final model. The same loss function used during training is often used for evaluation, although other metrics may also be relevant depending on the task.

Interpretation and Analysis: After the model is evaluated, the results are interpreted and analyzed. This can include looking at how much the model's predictions deviate from the true values, which features are most important for the model's predictions, whether the model is overfitting or underfitting the data, etc.

The process is then typically repeated, with adjustments made based on the results of the previous experiment, until a satisfactory model is obtained.