Energy Efficiency

Whether this result is one to rely on. Quality says how closely the formula follows the data; validity says whether that closeness means anything. A formula that only restates its target, or that reads a column which already holds the answer, can reach a very high quality and still tell you nothing new.

Data-quality, model-quality, and deployment-risk issues detected during the analysis appear below, ordered by severity. Critical concerns are listed first; Warning and Info entries follow.

One model per target, each a formula with its quality, complexity and error. Higher quality at lower complexity describes the data most clearly. The findings below read the models together; the per-target chapters in the Model section carry each formula, its predictions and its diagnostics.

The Model section presents one model per target: its formula, its predictions on held-out rows, the inputs it relies on, the baselines it is measured against, and diagnostics of how it behaves. With more than one target, the Composite Model, Multi-Output and Leaderboard chapters read the models as a set.

The three gauges score the model on the held-out rows: rows that were set aside before the search and that the model never saw. They are the figures to quote for how the model does on new data.

The figures under During the search are the same measures on the training rows. They are what the search ranked its candidates by, so they describe the search and tend to flatter the model it chose. The Generalization chapter sets the training rows beside the held-out rows, and the Baselines chapter sets the model beside its baselines. The time and credit gauges account for the computation that produced the model, not for the model itself.

Actual Heating load kwh m2 on the horizontal axis against the model's predicted value on the vertical axis, for the held-out rows the model never saw during training. Points on the diagonal are perfect predictions; systematic vertical offsets reveal bias, vertical spread reveals noise, and points far from the diagonal are rows the model handles poorly.

How the held-out residuals (actual Heating load kwh m2 minus predicted) are distributed. Bias is their mean: a value away from zero means the model is systematically high or low rather than merely imprecise. The standard deviation and the percentiles describe the spread, and the tail percentiles say how large the worst misses get. Every figure carries a bootstrap 95% confidence interval; with a small held-out set those intervals are wide, and that width is itself the finding.

The chart ranks the inputs of the Heating load kwh m2 model by permutation importance: how much the model's error rises when that input's values are shuffled across rows so that it carries no information. A longer bar means the model relies on the input more. The order says which columns the model reads most, and those are the columns where measurement quality and data collection matter most. A short bar marks an input the model barely uses, which is a fact about this model and not a verdict on the column. Importance describes the model's reliance and nothing more: an input can rank high because it stands in for something the data does not contain. Where the fit measured it, an input also carries the direction in which the model's output moves as the input rises, counted on the rows the search trained on, and the change of the output when the input alone goes from its first to its third quartile; both describe the formula inside the observed range and say nothing about causes.

The table scores the model for Heating load kwh m2 against simple yardsticks on the same held-out rows. A yardstick is a predictor simple enough to need no explanation: a constant (the average, the middle value, the most common class or level, the average count), a plain regression on the numeric inputs (a straight line, a logistic regression, a Poisson regression), and for a series over time a forecast from its own past (the last value, the value one season back, the recent trend extended). Which of them appear depends on what kind of column Heating load kwh m2 is. They are yardsticks only: the analysis has one model, and it is the last row. A regression yardstick answers every row the model answers: where one of its numeric inputs is empty, it reads the average of that input over the training rows. Nothing is filled in for the model. A yardstick whose row is empty could not be scored, and the summary then says what the margin is measured against.

Read the columns from top to bottom. Each kind of target is scored by the measure it is judged on: R² and MAE for a continuous value, with MASE added for a series (below 1 means a typical miss is smaller than the series' usual step from one row to the next); accuracy and balanced accuracy for a yes/no value, with the Brier score where a probability is predicted; accuracy and macro F1 for a class; weighted kappa and the distance in levels for an ordered level; Poisson deviance and RMSE for a count. When the model clears every yardstick by a wide margin, its structure earns its place. When it is level with the regression yardstick, a plain regression describes the data as well. When it is level with the constant, the inputs carry no usable signal for Heating load kwh m2.

The margin over the best yardstick comes with an interval. When that interval includes zero, the lead is not settled on this many held-out rows. The share of rows on which the model is closer than the best yardstick is counted only on the rows where the two differ; for a yes/no value or a class these are the rows where the two disagree.

The chart sets the R² of the Heating load kwh m2 model on the rows it trained on beside its R² on the held-out rows it never saw, and the gap between the two bars is the finding. The held-out bar carries a bootstrap 95% confidence interval, which says how far that figure could move with a different held-out draw; the training bar has none, because it is measured on the rows that shaped the model.

The verdict reads from the two figures. Generalizing: the held-out R² is strong, or training and held-out agree closely; the structure the formula encodes carries to new rows. Overfit: training is far ahead of held-out and the held-out R² is not strong on its own; the formula has absorbed noise from the training rows, and the training figure overstates what to expect on new data. Underfit or noisy: held-out is far ahead of training; this is not strength, it usually means an outlier or a flat region in the training rows that the held-out rows happen to avoid. Insufficient: fewer than 30 held-out rows and no strong held-out R², too little evidence for a negative verdict. In every case the width of the held-out interval says how much weight the gap can bear.

The formula for Heating load kwh m2 is split into its additive terms, and each term is traced as one of its inputs moves across the training range while the other inputs stay at their medians. Each curve is therefore a profile of the term at the typical row, not an average over the data: it shows what the term contributes at every value of that input when everything else is ordinary.

A term that depends on several inputs gets one curve per input; a constant term gets none. Terms the formula subtracts are drawn with their sign, so a curve below zero pulls the prediction down. At any fixed row, the terms add up to the model's prediction. Where the fit measured it, a term also carries its share of the variation of the model's output on the rows the search trained on; that is a share of what the formula returns, not of Heating load kwh m2 itself. The notebook lets the reader trim each range to the central 95% of the input. When the formula has no additive structure, the chapter traces the whole formula as a single term along each of its inputs, and the Sensitivity chapter is the better read for how the inputs combine.

The formula for Heating load kwh m2 is read as a mathematical object, without data, to state how it behaves beyond the range it was trained on. A black box cannot answer that question; a formula can. For each input the chapter reports the limit as the input grows without bound in either direction (whether the formula diverges, settles to a finite value or oscillates, with the sign tracked exactly, so that a term like minus two times the cube of the input is reported as diverging downward on the right and upward on the left), whether the formula stays finite in every direction, and any singularity with its solved location: a division whose denominator reaches zero, a logarithm or square root whose argument leaves its domain, or a periodic pole.

The inputs along which the formula diverges or meets a singularity are listed as the risky ones; along them the formula's shape gives no support for extrapolation. A formula that stays finite everywhere with no singularity carries no structural hazard when extrapolated; the data still ends where it ends, and a prediction outside the training range remains unsupported by evidence. The plain-language summary at the end states the same facts in one paragraph.

For up to five representative held-out rows, the chapter draws one bar chart showing how each additive term of the formula builds that row's prediction of Heating load kwh m2. The five rows are the worst prediction (largest absolute residual), the best (smallest), the median miss, the row with the smallest prediction and the row with the largest. When two roles fall on the same row, which is common with few held-out rows, the earlier role keeps it and fewer than five charts appear.

In each chart the bars stack the terms' contributions at the row's input values, terms the formula subtracts sit below zero, and the bars sum to the prediction. The dashed line marks the actual value; the distance between it and the top of the stack is the residual. The bars are evaluated at the same precision as the predictions, so they agree with the Prediction Chart. When the formula has no additive structure, each chart holds one bar for the whole formula, and the Sensitivity chapter is the better read for how individual inputs move it.

For each additive term of the formula for Heating load kwh m2, the chart shows how much the held-out R² drops when that term is replaced by its mean contribution, so that it no longer varies from row to row. The bars are sorted from the largest drop down, and the dashed line marks the R² of the full model.

A large drop means the term carries real predictive work; the complexity it adds is paid for. A small drop means the term adds little beyond its average value: it may refine a stronger term, or its curve in the chapter "How each term responds to its inputs" may be nearly flat. A negative drop means the held-out R² rises without the term, which is a sign that the term tracks noise in the training rows. Each figure describes what a term contributes inside the model as discovered; the chart diagnoses the model, it is not a guide to removing terms. When the formula has no additive structure, the chart shows one bar for the whole formula.

The chapter shows the model's prediction for Heating load kwh m2 at one input combination, with the contribution of each term stacked beneath it. The inputs start at their training medians, so the first view is the prediction for a typical row, and each input can move within the range the training rows cover; the notebook lets the reader change the inputs and watch the prediction and the stack update.

In the stack, a long bar marks the term that dominates at this input combination, often the one whose removal costs most in the chapter "What each term is worth". A short bar marks a term that makes a small adjustment here; the chapter "How each term responds to its inputs" shows whether it stays small everywhere or grows toward the edges of the range. A negative bar marks a term that pulls the prediction down at this point, either because the formula subtracts it or because it evaluates below zero.

The inputs stay inside the training range for a reason: the formula computes a value anywhere, but outside that range no training row supports it. When the formula has no additive structure, the stack holds a single bar for the whole formula and the inputs move the prediction directly.

For each input, the chart traces the rate at which the predicted Heating load kwh m2 changes as that input moves across its training range, with the other inputs held at their medians. The rate is the local slope of the prediction with respect to the input, measured by a small finite difference at each point. A table summarizes each input with the mean, minimum and maximum of the absolute slope, which ranks the inputs by how strongly the prediction responds to them.

A flat curve means the model is close to linear in that input: the prediction responds at the same rate everywhere in the observed range, which is easy to state and says nothing about values beyond that range. A curve that grows or shrinks marks diminishing or accelerating returns, and whether that is plausible is a question for the domain. A curve that crosses zero means the prediction rises with the input in one part of the range and falls in another, which is either a real optimum or a sign that the formula bends around a few rows. A curve with a large magnitude marks an input to which the prediction is highly responsive; the chapter "What each term is worth" says whether the term behind it also carries predictive work.

In the table, the mean absolute slope ranks the inputs by typical responsiveness. A minimum close to the maximum means the responsiveness is nearly constant; a wide gap means it varies strongly across the range. The chapter reads the whole formula, so it applies whether or not the formula splits into terms.

When a single term of the formula combines two or more inputs, the prediction's response to one of them depends on the value of the other. This chapter draws one surface for each such pair: the predicted Heating load kwh m2 across the plane of the two inputs, with every other input held at its training median. Pairs that never share a term have no interaction by construction, and the curves in the chapter "How each term responds to its inputs" already say everything about them. Where the fit tested a pair, the summary says on how many pairs of rows the two inputs acted together in the model's output; that is a statement about the formula, not a finding that the data hold no other interaction.

Parallel stripes mean the two inputs act almost independently, so the surface is close to a sum of two one-input curves. Curved contours mean a real interaction, where the slope along one input changes with the other; the location of the peak or trough matters. A saddle, rising along one axis and falling along the other, marks a trade-off between the two. A sharp edge or cliff means the formula encodes a change of regime, and the curve for the same input in the chapter "How each term responds to its inputs" shows whether the bend appears there too.

The grid is deliberately coarse, and the color scale runs from low to high predictions. When the formula has no additive structure, the single whole-formula term holds every input, so every pair appears; the number of surfaces is capped for models with many inputs.

The held-out rows on which the model misses Heating load kwh m2 by the most, sorted by absolute residual with the largest first and capped at ten. Each card shows the row's actual value, the prediction, the residual, the contribution of every additive term at that row and the row's input values. R² and MAE say how good the model is on average; these cards say where it fails and let each failure be read input by input and term by term.

A large residual with one dominant term means that term produced the wrong value at this row; the row's value for that input, read against its curve in the chapter "How each term responds to its inputs", shows whether it fell in a region the formula models poorly. A large residual with balanced contributions means every term was a little off and the sum still missed, which points to a shape the formula cannot represent in that region. Residuals that change sign from card to card mean the misses are not a consistent bias but scattered errors on particular rows. When the formula has no additive structure, each card shows a single whole-formula contribution.

Each held-out prediction of Heating load kwh m2 carries a prediction interval, and this chapter checks whether that interval covers the actual value as often as it claims. The interval reported with each prediction is built from the held-out residuals themselves: its bounds are the 2.5th and 97.5th percentiles of the residuals added to the prediction, so it is asymmetric when the residuals are skewed and assumes no particular error distribution.

The coverage table checks a second, simpler band: the symmetric interval that a normal error distribution with the residuals' standard deviation would give. At four nominal levels (50%, 80%, 90% and 95%) it lists the half-width of that normal band and the share of held-out rows whose actual value falls inside it. Empirical coverage close to nominal means the residuals are close enough to normal that the two bands agree and the interval can be taken at face value. Empirical coverage below nominal means the normal band is too narrow, the residuals have heavier tails than a normal distribution, and the percentile-based interval is the one to trust. Empirical coverage above nominal means the normal band is wider than the data needs, usually because a few large residuals inflate the standard deviation. Every figure comes from the same held-out residuals the intervals are built from.

Four residual diagnostics for Heating load kwh m2, all computed from the held-out residuals. Each asks in its own way whether the model's errors look like noise, which is what remains when a model has captured all the structure the data holds.

Residuals against predicted values: Each held-out row is plotted with the model's prediction on the horizontal axis and its residual on the vertical axis, around a zero line. A symmetric cloud around zero means errors of similar size across the predicted range and no systematic bias. A funnel or fan means the size of the errors depends on the predicted value: the model is more uncertain in some regions than in others, and its prediction interval is not equally trustworthy everywhere. A curved pattern, a smile or a frown, means the model misses a structural component; the chapters "How each term responds to its inputs" and "How two inputs act together" show the shapes the formula does capture.

Normal Q-Q plot: The sorted residuals are plotted against the quantiles of a normal distribution, with the diagonal marking a perfectly normal set of residuals. Points that hug the line mean approximately normal residuals, so the normal band in the Prediction Interval Coverage chapter will hold. An S-shape means heavier or lighter tails than normal; heavier tails (below the line at the left, above it at the right) mean the model occasionally produces large errors. A banana or arc means skewed residuals: the model is systematically high or low in part of the range.

Histogram: The residuals binned into equal-width intervals. A bell centered on zero means symmetric errors with no bias. An off-center bell means the model is biased, with a mean error away from zero. A long tail or two peaks mean outliers or two regimes inside the prediction range.

Autocorrelation: For each lag, the correlation of the residual sequence with itself shifted by that many rows, with the band that pure noise would stay inside at plus or minus 1.96 divided by the square root of the row count. Bars inside the band mean uncorrelated residuals with no order-dependent structure left. A bar at lag 1 outside the band means the residuals of neighbouring dates correlate: structure in time that the model has not captured. A wave across the lags means periodic structure remains, and the Time Series chapter in the Data section is where to look for its period.

Autocorrelation carries meaning only when the row order itself does. When the data has a date column, the held-out rows are the most recent ones in date order, and the autocorrelation is assessed. Without a date column the held-out rows are a random draw: the row after a held-out row is an arbitrary other row, so the autocorrelation is not assessed and the summary above says so.

The line traces the best quality the search for the Heating load kwh m2 model had reached at each generation, from the first generation to the last. Quality is the technology's combined score on the training rows, the figure the Model Metrics chapter defines. A curve that flattens well before the last generation means the search converged: the budget was more than enough, and the model is the one the search settled on. A curve still rising at the last generation means the budget ended before the search settled, and the model is the best the search reached within it. The chart describes the search, not the data: it says whether the search had time to settle, not whether more rows would help.

Sanity checks on the Heating load kwh m2 formula, run against the held-out rows. Three checks: every prediction is a finite number (output coherent), predictions stay within the range of the training target widened by two standard deviations on each side (within domain), and no single prediction runs away more than ten standard deviations from the training mean (bounded predictions).

These are pass or fail guards, not quality measures: a formula can clear all three and still predict poorly. A failure is the stronger signal. It means the formula misbehaves numerically somewhere in the data it was shown, and any downstream use of it should wait until that is understood.

The function below trains the model for Heating load kwh m2 on the processed data. Its output is the model that every other chapter of this section scores and dissects.

The Data section describes the table as supplied, before any modeling: the Column Profiles overview of every column and its role, one chapter per column with its distribution and correlations, a closer look at columns with notable characteristics, Duplicate Rows, Leakage Suspicion, a map for paired coordinate columns, and the General chapter with descriptive statistics, correlations, missing values, outlier ranges, clusters and segments across all columns.

One row per column of the analyzed table: its role in the analysis (the target being predicted, an input it is predicted from, or the segment column), its type, value count and missing count, and for numeric columns the mean, standard deviation, minimum, quartiles, maximum and interquartile range. A column with 25% or more missing values is flagged; its mean and quartiles describe only the rows that have a value.

Two further figures describe the shape of a numeric column. The skewness says whether the values lean to one side: close to zero the column is symmetric, from 0.5 it is moderately skewed and from 1 strongly skewed, with the longer tail on the high side when the figure is positive and on the low side when it is negative. In a strongly skewed column the mean is pulled toward the tail, and the median is the better guide to a typical value. The coefficient of variation is the standard deviation divided by the mean: it compares how widely columns spread regardless of their units, and is given only for a column whose mean is positive.

These are the columns as supplied, before any modeling: the reference against which every later chapter reads.

A column chapter profiles one column: its distribution in figures and charts, and how it relates to the other columns. It opens with one line on what the column holds. The Description chapter carries its figures, with every other column summarized for each of its values where it has few, and its association with every other column where it is numeric. The Visualization chapter carries its charts. A table with a date column adds an Over Time and a Time Series chapter; a target with classes adds a Class Balance chapter.

The figures below summarize Glazing area in numbers: where its values center (mean, median, mode), how far they spread (range, variance, standard deviation, interquartile range) and how they are distributed across percentiles. They are the reference for every chart in the Visualization chapter and for the correlation measures further down.

The figures for Glazing area are grouped: the column itself first, then where its values center, how far they spread, the shape of their distribution and its percentiles. Each statistic is explained in the Description chapter under General in the Data section.

The rows are grouped by the value of Glazing area, and every other column is summarized within each group with the same descriptive statistics. A statistic that shifts from group to group marks a column that moves with Glazing area; one that stays level marks a column that does not. Groups with few rows produce unstable figures, so the row count of each group is the first thing to read. Where the groups differ in a target by more than chance would give, the chapter states by how much; it states that the two go together, not that one brings the other about.

Each row pairs Glazing area with one other column, numeric or categorical, and reports how strongly the two go together on an association from 0 to 1, and whether an association this strong could be chance. For another numeric column the row adds the direction: Pearson's coefficient measures a straight-line relationship, and Spearman's rho and Kendall's tau measure a monotonic relationship on ranks, which makes them resistant to outliers and lets them see a curved but consistently rising or falling pattern. For a categorical column the association is the correlation ratio η, which has no direction. A strong association is not an explanation: two columns can go together when a third one moves both.

The table lists every other numeric or categorical column against Glazing area, with the pair's kind and association, three correlation coefficients and a confidence interval where the other column is numeric, the q-value and the rows the pair was measured on.

The charts in this chapter were chosen from the type of Glazing area and of the columns it is compared with: a numeric column gets a histogram, a box plot and, when its row order carries a pattern, a value sequence, a categorical column gets a frequency chart, and its relation to each target of the analysis, and to the segment column when there is one, gets the chart that suits the pair, with the target on the vertical axis where it is a number. A column is not charted against every other column; which columns move together is shown under Strongest Correlations. The charts complement the figures in the Description chapter; the shape of a distribution and the position of its outliers are easier to see than to read.

This chapter counts rows that repeat another row exactly, value for value: how many rows take part in a duplicate group, how many groups exist, and how large the largest group is.

Duplicate rows inflate the apparent row count and can place identical rows on both sides of the training and held-out split, which flatters every quality figure in this report. Only exact repeats are detected here; rows that differ by a rounding digit or a whitespace variant count as distinct.

For every column that is not a target, this chapter reads how closely the column tracks each target, on an association from 0 to 1, and lists any pair at 0.95 or more. For two numeric columns the association is the stronger of Pearson's r and Spearman's rho; when the column or the target is categorical it is the correlation ratio η, or Cramér's V when both are. At 0.999 or more the column reproduces the target: that is what a copy or a rescaled copy of it looks like.

A listed column poses one question: is its value known before the target's value exists? If it is, the column is a strong predictor and the quality stated in this report is real. If it was computed from the target or recorded after it, a formula that reads it looks right on these rows and will not hold on new data. The coefficients read the same in both cases; the answer needs someone who knows where the column came from.

The owner of the analysis can give that answer. A column confirmed as known before the outcome is listed as confirmed and is no longer a suspect. A column that turns out to be a leak is left out of the fit, and the analysis run again.

The General chapter covers what holds across all columns together: descriptive statistics, correlations, missing values and outlier ranges under Description, the Clusters found among the rows, and, when a segment column was chosen, the Segments.

This chapter summarizes every column at once: the descriptive statistics table below, then Correlation, Missing Values and Outliers. For a numeric column the table reports its center (mean, median, mode), its spread (standard deviation, variance, interquartile range, percentiles) and its shape (skewness, kurtosis); for a categorical column it reports the count and share of each category.

Each row of the tables describes one column. The statistics are grouped: the column itself, where its values center, how far they spread, what shape their distribution takes, and its percentiles. They read as follows.

The table lists, for each column, the count of present values (Values) beside the row count of the processed table (Rows), the number of missing values and their share. The larger the share, the less any statistic or model built on the column can be trusted.

• Below 5% missing: safe to use as it is.
• 5% to 25% missing: usable; filling the gaps or excluding those rows is worth considering.
• 25% or more missing: the column is flagged and receives its own chapter in the Data section. Verify why so much is missing before trusting any result that depends on it.

A model is computed only on rows that hold a value in every column it reads, so gaps spread over several columns cost more rows than any one column's share suggests. The last column, Complete rows without, shows for each input with gaps how many rows would be complete if that column were left out; it is blank for a column without gaps, for a target, and for a column no model reads. A column that is the only gap in many rows is the one whose removal keeps the most data.

The table counts the outliers of every numeric column by the Tukey rule. Q1 and Q3 are the values below which 25% and 75% of a column's values fall, and the interquartile range is Q3 minus Q1. The lower fence lies 1.5 times the interquartile range below Q1, the upper fence the same distance above Q3; a value beyond a fence is an outlier. For each column the table gives both fences, how many values lie below and above them, their share of the column's values, and the single value that lies furthest beyond its fence. These are the same fences the box plots draw their whiskers to.

A column is not assessed when it has fewer than four values, or when the middle half of its values sits on a single number: the interquartile range is then zero and the rule would call every other value an outlier.

Extreme values can be real (rare but legitimate rows) or errors (measurement mistakes, data-entry slips). Which case applies decides whether to keep, clip or drop them before trusting a model that uses the column. A strongly skewed column has many values beyond one fence without any of them being wrong.

This chapter measures how pairs of columns go together: the Correlation Measures table below, the Strongest Correlations, the Correlation Heatmap and, when the analysis has targets, the Potential Data Leaks. Numeric columns and categorical columns are both paired, a categorical column being one that is not numeric and holds between 2 and 50 distinct values. Every pair is stated as an association from 0 (unrelated) to 1 (one column gives the other away), so pairs of different kinds can be compared. An association states that two columns go together, not that one brings the other about.

The table lists every pair of columns once, with its kind, its association, the figures of its kind, its q-value and the number of rows the pair was measured on. A pair is measured on the rows where both columns hold a value.

The Implications section states how to act on the models: the Stakeholder Summary and the Recommended Next Data, where the models hold and where they weaken (Quality by Input Range, Rows unlike the ones the model learned from, Per-Segment Predictions, Fairness), what to weigh before relying on them (Causal Honesty, Deployment Readiness), and the Provenance & Audit trail a reviewer needs to retrace the analysis.

Out-of-distribution detection finds held-out rows that lie far from the training rows of a model. It looks only at the numeric inputs the model reads. Each of them is standardized against the mean and standard deviation of the fit rows, and the standardized values are combined into one distance per row. The line a row is read against depends on the number of inputs: it is the distance that 99 in 100 rows like the fit rows stay below. A row beyond the line is flagged as out of distribution, and the held-out figures are unlikely to apply to it. When the held-out rows resemble the fit rows, about one row in a hundred is flagged.

The chart shows one bar per held-out row in row order; the flagged rows are the bars at or above the line. With more than one target, the chart shows the model with the largest flagged share, and the figures name it.

The check treats inputs independently, so it will not notice a rare combination of values that are each ordinary on their own, such as a large height with a small weight. It is a first screen. A decision that depends on catching unusual inputs needs a dedicated check.