# Glossary

- Alert
An alert is an indication of whether a particular statistic calculated by NannyML is abnormal and possibly warrants further investigation. During data quality, drift or performance calculations lower and upper thresholds can be specified to restrain the expected range of the metric being calculated or estimated. An alert is raised after NannyML finds the calculated metric outside of the specified range.

Note that alerts are not raised during the reference Data Period.

- Business Value Matrix
A matrix that is used to calculate the business value of a model. The format of the business value matrix must be specified so that each element represents the business value of it’s respective confusion matrix element. Hence the element on the i-th row and j-column of the business value matrix tells us the value of the i-th target when we have predicted the j-th value. It can be provided as a list of lists or a numpy array. The business value of a model is calculated as the sum of the products of the values in the matrix and the corresponding cells in the confusion matrix.

For more information about the business value matrix, check out the Business Value “How it Works” page.

- Butterfly dataset
A dataset used in Multivariate Drift Detection to give an example where univariate drift statistics are insufficient in detecting complex data drifts in multidimensional data.

- CBPE (Confidence-Based Performance Estimation)
A family of methods to estimate classification model performance in the absence of ground truth that takes advantage of the confidence which is expressed in the monitored model output probability/score prediction. To see how it works, check out our CBPE deep dive.

- Chi Squared test
The Chi Squared test, or chi2 test as is sometimes called, is a non-parametric statistical test regarding discrete distributions. It is used to examine whether there is a statistically significant difference between expected and observed frequencies for one or more categories of a contingency table. In NannyML, we use the Chi Squared test to answer whether the two samples of a categorical variable come from a different distribution.

The Chi Squared test results include the chi squared statistic and a p-value. The bigger the chi squared statistic, the more different the results between the two samples we are comparing. The p-value represents the chance that we would get the results we have provided if they came from the same distribution.

You can find more information on the wikipedia Chi-squared test page. At NannyML, we use the scipy implementation of the Chi-square test of independence of variables in a contingency table.

- Child model
Another name for the monitored model. It is used when describing solutions for which NannyML trains its own model called nanny model.

- Concept Drift
A change in the underlying pattern (or mapping) between the Model Inputs and the Target (P(Y|X)).

- Confidence Band
When we estimate a statistic from a sample, our estimation has to take into account the variance of that statistic from its sampled distribution. We do that by calculating Sampling Error. When we visualize our results, we show a Confidence Band above and below our estimation. This confidence band comprises the values that have a distance less than the sampling error from our estimation. This helps us know when changes in the value of a statistic are statistically significant instead of happening due to the natural variance of the statistic.

Note that the confidence band is also described as the sampling error range at the hover information that appears on the interactive plots.

- Confidence Score
A score that is returned by the classification model together with class prediction. It expresses the confidence of the prediction i.e. the closer the score is to its minimum or maximum, the more confident the classifier is with its prediction. If the score is in the range between 0 and 1, it is called a

*probability estimate*. It can also be the actual*probability*. Regardless of the algorithm type, all classification models calculate some form of confidence scores. These scores are then thresholded to return the predicted class. Confidence scores can be turned into calibrated probabilities and used to estimate the performance of classification models in the absence of ground truth, to learn more about this check out our Confidence-based Performance Estimation Deep Dive.- Confusion Matrix
A confusion matrix is a table that is often used to describe the performance of a classification model (or a set of classifiers). Each row of the matrix represents the instances in an actual class while each column represents the instances in a predicted class. In binary classification the matrix has 4 cells, that are commonly named as follows: true positives (TP), true negatives (TN), false positives (FP) and false negatives (FN). For more information on the confusion matrix, see the Wikipedia Confusion Matrix page.

- Covariate Shift
A change in the distribution of Model Inputs, \(P(\mathbf{X})\). Note that under covariate shift while the distribution of model inputs changes the conditional probability \(P(Y|\mathbf{X})\) does not change. The latter is called Concept Drift.

- Data Drift
A change in joint distribution of Model Inputs and model targets, denoted as \(P(\mathbf{X}, Y)\).

- Data Chunk
A data chunk is simply a sample of data. All the results generated by NannyML are calculated and presented on the chunk level i.e. a chunk is a single data point on the monitoring results. Chunks are usually created based on time periods - they contain all the observations and predictions from a single hour, day, month etc. depending on the selected interval. They can also be size-based so that each chunk contains

*n*observations or number-based so the whole data is split into*k*chunks. In each case chronology of data between chunks is maintained. To better understand how to create chunks with NannyML check out the chunking tutorial.- Data Period
A data period is a subset of the data used to monitor a model. NannyML expects the provided data to be in one of two data periods.

The first data period is called the

**reference**period. It contains all the observations for a period with an*accepted*level of performance. It most likely also includes**target**data. This period can be the test set for a model that only recently entered production or a selected benchmark dataset for a model that has been in production for some time.The second subset of the data is the

**analysis**period. It contains the observations you want NannyML to analyse. In the absence of targets, performance in the analysis period can be estimated.You can read more about Data Periods in the relevant data requirements section.

- Domain Classifier
A domain classifer is a machine learning classification model trained to identify whether a given data point belongs to one or another dataset. NannyML uses domain classifers as a multivariate drift detection method. You can read more about them in How it works: Domain Classifier and see how to use them in Tutorial: Domain Classifier.

- Error
The error of a statistic on a sample is defined as the difference between the value of the observation and the true value. The sample size can sometimes be 1 but it is usually bigger. When the error consists only of the effects of sampling, we call it sampling error.

- Estimated Performance
The performance the monitored model is expected to have as a result of the Performance Estimation process. Estimated performance can be available immediately after predictions are made.

- Feature
A variable used by our machine learning model. The model inputs consist of features.

- Label
A synonym for Target.

- Latent space
A space of reduced dimensionality, compared to the model input space, that can represent our input data. This space is the result of a representation learning algorithm. Data points that are close together in the model input space are also close together in the latent space.

- Ground truth
A synonym for Target.

- Identifier
Usually a single column, but can be multiple columns where necessary. It is used uniquely identify an observation. When providing Target data at a later point in time, this value can help refer back to the original prediction.

Being able to uniquely identify each row of data can help reference any particular issues NannyML might identify and make resolving issues easier for you. As we add functionality to provide

**target**data afterwards your data will already be in the correct shape to support it!Note

**Format**No specific format. Any str or int value is possible.

**Candidates**An existing identifier from your business case. A technical identifier such as a globally unique identifier (GUID). A hash of some (or all) of your column values, using a hashing function with appropriate collision properties, e.g. the SHA-2 and SHA-3 families. A concatenation of your dataset name and a row number.

- Imputation
The process of substituting missing values with actual values on a dataset.

- Kolmogorov-Smirnov test
The Kolmogorov-Smirnov test, or KS test as it is more commonly called, is a non-parametric statistical test regarding the equality of continuous one-dimensional probability distributions. It can be used to compare a sample with a reference probability distribution, called one-sample KS test, or to compare two samples. In NannyML, we use the two-sample KS test looking to answer whether the two samples in question come from a different distribution.

The KS test results include the KS statistic, or d-statistic as it is more commonly called, and a p-value. The d-statistic takes values between 0 and 1. The bigger the d-statistic, the more different the results between the two samples we are comparing are. The p value represents the chance that we would get the results we have provided if they come from the same distribution.

You can find more information on the wikipedia KS test page. At NannyML, we use the scipy implementation of the two sample KS test.

- Loss
Loss is a real number that quantifies the negative aspects associated with an event. It is defined by a Loss Function that, for the purposes of Model Monitoring, comes from a specified performance metric. NannyML uses loss for Performance Estimation for Regression with the constraint that the Loss Function is positive.

- Loss Function
A loss function is a function that maps the residuals to a real number that represents a loss associated with the event.

- Model inputs
Every Feature used by the model.

- Model outputs
The scores or probabilities that your model predicts for its target outcome.

- Model predictions
A synonym for Model outputs.

- Multivariate Drift Detection
Drift Detection steps that involve all model features in order to create appropriate drift measures.

- Nanny model
An extra model created by NannyML as part of its monitoring solution. The name is used to distinguish from the monitored model, which is sometimes referred to as child model.

- Partition Column
A column that tells us what Data Period the data is in. A partition column is necessary for NannyML in order to produce model monitoring results.

- PCA
Principal Component Analysis is a method used for dimensionality reduction. The method produces a linear transformation of the input data that results in a space with orthogonal components that maximise the available variance of the input data.

More information is available on the PCA Wikipedia page.

- Performance Estimation
Estimating the performance of a deployed ML model without having access to Target.

- Predictions
A synonym for Model outputs.

- Predicted labels
The outcome a machine learning model predicts for the event it was called to predict. Predicted labels are a two value categorical variable. They can be represented by integers, usually 0 and 1, booleans, meaning True or False, or strings. For NannyML, in a binary classification problem, it is ideal if predicted labels are presented as integers, with 1 representing the positive outcome.

- Predicted probabilities
The probabilities assigned by a machine learning model regarding the chance that a positive event materializes for the binary outcome it was called to predict.

- Predicted scores
Sometimes the prediction of a machine learning model is transformed into a continuous range of real numbers. Those scores take values outside the [0,1] range that is allowed for probabilities. The higher the score, the more likely the positive outcome should be.

- Ranking
NannyML uses ranking to order columns in univariate drift results. The resulting order can be helpful in prioritizing what to further investigate if needed. More information can be found in the ranking tutorial and how it works pages.

- Realized Performance
The actual performance of the monitored model once Targets become available. The term is used to differentiate between Estimated Performance and actual results.

- Reconstruction Error
The average Euclidean distance between the original and the reconstructed data points in a dataset. The reconstructed dataset is created by transforming our model inputs to a Latent space and

then transforming them back to the model input space. Given that this process cannot be lossless, there will always be a difference between the original and the reconstructed data. This difference is captured by the reconstruction error.

- Residual
The residual of a statistic on a sample is defined as the difference between the value of the observation and the expected value. The sample size can sometimes be 1 but it is usually bigger. For example the mean squared error regression metric could also be called mean squared residual because it uses the difference between the expected value (y_pred) and the observed results (y_true).

- Sampling Error
Sampling errors are statistical errors that arise when a sample does not accurately represent the whole population. They are the difference between the real values of the population, which we don’t always know, and the values derived by using samples from the population. In order to quantify the sampling error we use the Standard Error. You can find more about how NannyML calculates sampling error at Calculating Sampling Error.

- Standard Error
The Standard Error of a statistic is the standard deviation of the probability distribution we are sampling it from. It can also be an estimate of that standard deviation. If the statistic is the sample mean, then it is called Standard Error of the Mean and abbreviated as SEM.

The exact value of standard error from an independent sample of \(n\) observations taken from a statistical population with standard deviation \(\sigma\) is:

\[{\sigma }_{\bar {x}}\ ={\frac {\sigma }{\sqrt {n}}}\]Knowing the standard error of a statistic, we can calculate an appropriate range of values where the true value of the statistic lies with a given probability. More information can be read at the Wikipedia Standard Error page.

- Target
The actual outcome of the event the machine learning model is trying to predict. Also referred to as Ground truth or Label.

- Timestamp
Usually a single column, but it can be multiple columns where necessary. This provides NannyML with the date and time that the prediction was made.

NannyML needs to understand when predictions were made and how you record this, so it can bucket observations in time periods.

Note

**Format**Any format supported by Pandas, most likely:

*ISO 8601*, e.g.`2021-10-13T08:47:23Z`

*Unix-epoch*in units of seconds, e.g.`1513393355`

- Threshold
A threshold is an upper or lower limit for the normally expected values of a drift method, data quality metric or performance metric. Outside of the range defined by the threshold values we classify the calculated value of the method or metric as abnormal in which case an Alert is raised.

- Univariate Drift Detection
Drift Detection methods that use each model feature individually in order to detect change.

- Unseen Values
NannyML uses Unseen Values as a data quality check for categorical features. This is done in two steps. By looking at the reference Data Period a set of expected is created for each categorical feature. The second step is looking at the values present in the analysis Data Period for each categorical feature, any value not previously seen on the reference period is considered Unseen Value. You can find more information at the Unseen Values Detection tutorial.