Benchmarking Lag-Llama in opposition to XGBoost
On Hugging Face, there are 20 fashions tagged “time sequence” on the time of writing. Whereas definitely not lots (the “text-generation-inference” tag yields 125,950 outcomes), time sequence forecasting with basis fashions is an attention-grabbing sufficient area of interest for large firms like Amazon, IBM and Salesforce to have developed their very own fashions: Chronos, TinyTimeMixer and Moirai, respectively. On the time of writing, one of the vital widespread on Hugging Face by variety of likes is Lag-Llama, a univariate probabilistic mannequin. Developed by Kashif Rasul, Arjun Ashok and co-authors [1], Lag-Llama was open sourced in February 2024. The authors of the mannequin declare “robust zero-shot generalization capabilities” on quite a lot of datasets throughout completely different domains. As soon as fine-tuned for particular duties, additionally they declare it to be the very best general-purpose mannequin of its form. Huge phrases!
On this weblog, I showcase my expertise fine-tuning Lag-Llama, and check its capabilities in opposition to a extra classical machine studying method. Particularly, I benchmark it in opposition to an XGBoost mannequin designed to deal with univariate time sequence knowledge. Gradient boosting algorithms resembling XGBoost are extensively thought of the epitome of “classical” machine studying (versus deep-learning), and have been proven to carry out extraordinarily effectively with tabular knowledge [2]. Due to this fact, it appears becoming to make use of XGBoost to check if Lag-Llama lives as much as its guarantees. Will the muse mannequin do higher? Spoiler alert: it isn’t that straightforward.
By the way in which, I can’t go into the small print of the mannequin structure, however the paper is value a learn, as is that this good walk-through by Marco Peixeiro.
The info that I take advantage of for this train is a 4-year-long sequence of hourly wave heights off the coast of Ribadesella, a city within the Spanish area of Asturias. The sequence is on the market on the Spanish ports authority knowledge portal. The measurements have been taken at a station situated within the coordinates (43.5, -5.083), from 18/06/2020 00:00 to 18/06/2024 23:00 [3]. I’ve determined to mixture the sequence to a every day degree, taking the max over the 24 observations in every day. The reason being that the ideas that we undergo on this publish are higher illustrated from a barely much less granular perspective. In any other case, the outcomes turn into very risky in a short time. Due to this fact, our goal variable is the utmost peak of the waves recorded in a day, measured in meters.
There are a number of the explanation why I selected this sequence: the primary one is that the Lag-Llama mannequin was skilled on some weather-related knowledge, though not lots, comparatively. I’d anticipate the mannequin to seek out any such knowledge barely difficult, however nonetheless manageable. The second is that, whereas meteorological forecasts are sometimes produced utilizing numerical climate fashions, statistical fashions can nonetheless complement these forecasts, specifically for long-range predictions. On the very least, within the period of local weather change, I feel statistical fashions can inform us what we might sometimes anticipate, and the way far off it’s from what is definitely occurring.
The dataset is fairly normal and doesn’t require a lot preprocessing aside from imputing a number of lacking values. The plot under exhibits what it seems to be like after we break up it into practice, validation and check units. The final two units have a size of 5 months. To know extra about how we preprocess the information, take a look at this pocket book.
We’re going to benchmark Lag-Llama in opposition to XGBoost on two univariate forecasting duties: level forecasting and probabilistic forecasting. The 2 duties complement one another: level forecasting offers us a selected, single-number prediction, whereas probabilistic forecasting offers us a confidence area round it. One might say that Lag-Llama was solely skilled for the latter, so we must always concentrate on that one. Whereas that’s true, I imagine that people discover it simpler to know a single quantity than a confidence interval, so I feel the purpose forecast continues to be helpful, even when only for illustrative functions.
There are a lot of components that we have to think about when producing a forecast. A few of the most essential embody the forecast horizon, the final statement(s) that we feed the mannequin, or how typically we replace the mannequin (if in any respect). Completely different mixtures of things yield their very own varieties of forecast with their very own interpretations. In our case, we’re going to do a recursive multi-step forecast with out updating the mannequin, with a step dimension of seven days. Because of this we’re going to use one single mannequin to provide batches of seven forecasts at a time. After producing one batch, the mannequin sees 7 extra knowledge factors, akin to the dates that it simply predicted, and it produces 7 extra forecasts. The mannequin, nonetheless, will not be retrained as new knowledge is on the market. When it comes to our dataset, which means we are going to produce a forecast of most wave heights for every day of the subsequent week.
For level forecasting, we’re going to use the Imply Absolute Error (MAE) as efficiency metric. Within the case of probabilistic forecasting, we are going to goal for empirical protection or protection chance of 80%.
The scene is ready. Let’s get our arms soiled with the experiments!
Whereas initially not designed for time sequence forecasting, gradient boosting algorithms typically, and XGBoost particularly, will be nice predictors. We simply must feed the algorithm the information in the fitting format. For example, if we need to use three lags of our goal sequence, we are able to merely create three columns (say, in a pandas dataframe) with the lagged values and voilà! An XGBoost forecaster. Nonetheless, this course of can rapidly turn into onerous, particularly if we intend to make use of many lags. Fortunately for us, the library Skforecast [4] can do that. In actual fact, Skforecast is the one-stop store for creating and testing all types of forecasters. I truthfully can’t suggest it sufficient!
Making a forecaster with Skforecast is fairly simple. We simply must create a ForecasterAutoreg object with an XGBoost regressor, which we are able to then fine-tune. On prime of the XGBoost hyperparamters that we might sometimes optimise for, we additionally must seek for the very best variety of lags to incorporate in our mannequin. To do this, Skforecast supplies a Bayesian optimisation technique that runs Optuna on the background, bayesian_search_forecaster.
The search yields an optimised XGBoost forecaster which, amongst different hyperparameters, makes use of 21 lags of the goal variable, i.e. 21 days of most wave heights to foretell the subsequent:
Lags: [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21]
Parameters: {'n_estimators': 900,
'max_depth': 12,
'learning_rate': 0.30394338985367425,
'reg_alpha': 0.5,
'reg_lambda': 0.0,
'subsample': 1.0,
'colsample_bytree': 0.2}
However is the mannequin any good? Let’s discover out!
Level forecasting
First, let’s have a look at how effectively the XGBoost forecaster does at predicting the subsequent 7 days of most wave heights. The chart under plots the predictions in opposition to the precise values of our check set. We will see that the prediction tends to comply with the overall pattern of the particular knowledge, however it’s removed from excellent.
To create the predictions depicted above, we’ve got used Skforecast’s backtesting_forecaster perform, which permits us to guage the mannequin on a check set, as proven within the following code snippet. On prime of the predictions, we additionally get a efficiency metric, which in our case is the MAE.
Our mannequin’s MAE is 0.64. Because of this, on common, our predictions are 64cm off the precise measurement. To place this worth in context, the usual deviation of the goal variable is 0.86. Due to this fact, our mannequin’s common error is about 0.74 items of the usual deviation. Moreover, if we have been to easily use the earlier equal statement as a dummy finest guess for our forecast, we might get a MAE of 0.84 (see level 1 of this pocket book). All issues thought of, plainly, to date, our mannequin is healthier than a easy logical rule, which is a reduction!
Probabilistic forecasting
Skforecast permits us to calculate distribution intervals the place the longer term end result is prone to fall. The library supplies two strategies: utilizing both bootstrapped residuals or quantile regression. The outcomes will not be very completely different, so I’m going to focus right here on the bootstrapped residuals technique. You may see extra ends in half 3 of this pocket book.
The thought of developing prediction intervals utilizing bootstrapped residuals is that we are able to randomly take a mannequin’s forecast errors (residuals) an add them to the identical mannequin’s forecasts. By repeating the method a variety of instances, we are able to assemble an equal variety of various forecasts. These predictions comply with a distribution that we are able to get prediction intervals from. In different phrases, if we assume that the forecast errors are random and identically distributed in time, including these errors creates a universe of equally attainable forecasts. On this universe, we might anticipate to see at the very least a share of the particular values of the forecasted sequence. In our case, we are going to goal for 80% of the values (that’s, a protection of 80%).
To assemble the prediction intervals with Skforecast, we comply with a 3-step course of: first, we generate forecasts for our validation set; second, we compute the residuals from these forecasts and retailer them in our forecaster class; third, we get the probabilistic forecasts for our check set. The second and third steps are illustrated within the snippet under (the primary one corresponds to the code snippet within the earlier part). Traces 14-17 are the parameters that govern our bootstrap calculation.
The ensuing prediction intervals are depicted within the chart under.
An 84.67% of values within the check set fall inside our prediction intervals, which is simply above our goal of 80%. Whereas this isn’t unhealthy, it might additionally imply that we’re overshooting and our intervals are too large. Consider it this manner: if we mentioned that tomorrow’s waves could be between 0 and infinity meters excessive, we might at all times be proper, however the forecast could be ineffective! To get a thought of how large our intervals are, Skforecast’s docs recommend that we compute the world of our intervals by thaking the sum of the variations between the higher and decrease boundaries of the intervals. This isn’t an absolute measure, however it could assist us examine throughout forecasters. In our case, the world is 348.28.
These are our XGBoost outcomes. How about Lag-Llama?
The authors of Lag-Llama present a demo pocket book to start out forecasting with the mannequin with out fine-tuning it. The code is able to produce probabilistic forecasts given a set horizon, or prediction size, and a context size, or the quantity of earlier knowledge factors to contemplate within the forecast. We simply must name the get_llama_predictions perform under:
The core of the funtion is a LagLlamaEstimatorclass (traces 19–47), which is a Pytorch Lightning Estimator primarily based on the GluonTS [5] package deal for probabilistic forecasting. I recommend you undergo the GluonTS docs to get acquainted with the package deal.
We will leverage the get_llama_predictions perform to provide recursive multistep forecasts. We merely want to provide batches of predictions over consecutive batches. That is what we do within the perform under, recursive_forecast:
In traces 37 to 39 of the code snippet above, we extract the percentiles 10 and 90 to provide an 80% probabilistic forecast (90–10), in addition to the median of the probabilistic prediction to get some extent forecast. If you could study extra concerning the output of the mannequin, I recommend you take a look on the writer’s tutorial talked about above.
The authors of the mannequin advise that completely different datasets and forecasting duties might require differen context lenghts. In our case, we attempt context lenghts of 32, 64 and 128 tokens (lags). The chart under exhibits the outcomes of the 64-token mannequin.
Level forecasting
As we mentioned above, Lag-Llama will not be meant to calculate level forecasts, however we are able to get one by taking the median of the probabilistic interval that it returns. One other potential level forecast could be the imply, though it could be topic to outliers within the interval. In any case, for our explicit dataset, each choices yield comparable outcomes.
The MAE of the 32-token mannequin was 0.75. That of the 64-token mannequin was 0.77, whereas the MAE of the 128-token mannequin was 0.77 as effectively. These are all greater than the XGBoost forecaster’s, which went right down to 0.64. In actual fact, they’re very near the baseline, dummy mannequin that used the earlier week’s worth as as we speak’s forecast (MAE 0.84).
Probabilistic forecasting
With a predicted interval protection of 68.67% and an interval space of 280.05, the 32-token forecast doesn’t carry out as much as our required normal. The 64-token one, reaches an 74.0% protection, which will get nearer to the 80% area that we’re searching for. To take action, it takes an interval space of 343.74. The 128-token mannequin overshoots however is nearer to the mark, with an 84.67% protection and an space of 399.25. We will grasp an attention-grabbing pattern right here: extra protection implies a bigger interval space. This could not at all times be the case — a really slim interval might at all times be proper. Nonetheless, in apply this trade-off may be very a lot current in all of the fashions I’ve skilled.
Discover the periodic bulges within the chart (round March 10 or April 7, for example). Since we’re producing a 7-day forecast, the bulges symbolize the elevated uncertainty as we transfer away from the final statement that the mannequin noticed. In different phrases, a forecast for the subsequent day might be much less unsure than a forecast for the day after subsequent, and so forth.
The 128-token mannequin yields very comparable outcomes to the XGBoost forecaster, which had an space 348.28 and a protection of 84.67%. Primarily based on these outcomes, we are able to say that, with no coaching, Lag-Llama’s efficiency is fairly stable and as much as par with an optimised conventional forecaster.
Lag-Llama’s Github repo comes with a “finest practices” part with ideas to make use of and fine-tune the mannequin. The authors particularly suggest tuning the context size and the training price. We’re going to discover among the prompt values for these hyperparameters. The code snippet under, which I’ve taken and modified from the authors’ fine-tuning tutorial pocket book, exhibits how we are able to conduct a small grid search:
Within the code above, we loop over context lengths of 32, 64, and 128 tokens, in addition to studying charges of 0.001, 0.001, and 0.005. Inside the loop, we additionally calculate some check metrics: Protection[0.8], Protection[0.9] and Imply Absolute Error of (MAE) Protection. Protection[0.x] measures what number of predictions fall inside their prediction interval. For example, a superb mannequin ought to have a Protection[0.8] of round 80%. MAE Protection, however, measures the deviation of the particular protection possibilities from the nominal protection ranges. Due to this fact, a superb mannequin in our case needs to be one with a small MAE and coverages of round 80% and 90%, respectively.
One of many primary variations with respect to the unique fine-tuning code from the authors is line 46. In that line, the unique code doesn’t embody a validation set. In my expertise, not together with it meant that each one fashions that I skilled ended up overfitting the coaching knowledge. Alternatively, with a validation set most fashions have been optimised in Epoch 0 and didn’t enhance the validation loss thereafter. With extra knowledge, we might even see much less excessive outcomes.
As soon as skilled, a lot of the fashions within the loop yield a MAE of 0.5 and coverages of 1 on the check set. Because of this the fashions have very broad prediction intervals, however the prediction will not be very exact. The mannequin that strikes a greater steadiness is mannequin 6 (counting from 0 to eight within the loop), with the next hyperparameters and metrics:
{'context_length': 128,
'lr': 0.001,
'Protection[0.8]': 0.7142857142857143,
'Protection[0.9]': 0.8571428571428571,
'MAE_Coverage': 0.36666666666666664}
Since that is essentially the most promising mannequin, we’re going to run it by way of the exams that we’ve got with the opposite forecasters.
The chart under exhibits the predictions from the fine-tuned mannequin.
One thing that catches the attention in a short time is that prediction intervals are considerably smaller than these from the zero-shot model. In actual fact, the interval space is 188.69. With these prediction intervals, the mannequin reaches a protection of 56.67% over the 7-day recursive forecast. Keep in mind that our greatest zero-shot predictions, with a 128-token context, had an space of 399.25, reaching a protection of 84.67%. This implies a 55% discount within the interval space, with solely a 33% lower in protection. Nonetheless, the fine-tuned mannequin is simply too removed from the 80% protection that we’re aiming for, whereas the zero-shot mannequin with 128 tokens wasn’t.
Relating to level forecasting, the MAE of the mannequin is 0.77, which isn’t an enchancment over the zero-shot forecasts and worse than the XGBoost forecaster.
Total, the fine-tuned mannequin leaves doesn’t go away us a superb image: it doesn’t do higher than a zero-shot higher at both level of probabilistic forecasting. The authors do recommend that the mannequin can enhance if fine-tuned with extra knowledge, so it might be that our coaching set was not massive sufficient.
To recap, let’s ask once more the query that we set out at the start of this weblog: Is Lag-Llama higher at forecasting than XGBoost? For our dataset, the quick reply is not any, they’re comparable. The lengthy reply is extra difficult, although. Zero-shot forecasts with a 128-token context size have been on the similar degree as XGBoost by way of probabilistic forecasting. Superb-tuning Lag-Llama additional decreased the prediction space, making the mannequin’s appropriate forecasts extra exact, albeit at a considerable price by way of probabilistc protection. This raises the query of the place the mannequin might get with extra coaching knowledge. However extra knowledge we didn’t have, so we are able to’t say that Lag-Llama beat XGBoost.
These outcomes inevitably open a broader debate: since one will not be higher than the opposite by way of efficiency, which one ought to we use? On this case, we’d want to contemplate different variables resembling ease of use, deployment and upkeep and inference prices. Whereas I haven’t formally examined the 2 choices in any of these features, I believe the XGBoost would come out higher. Much less data- and resource-hungry, fairly sturdy to overfitting and time-tested are hard-to-beat traits, and XGBoost has all of them.
However don’t imagine me! The code that I used is publicly accessible on this Github repo, so go take a look and run it your self.
