Benchmarking Lag-Llama in opposition to XGBoost
On Hugging Face, there are 20 fashions tagged “time collection” on the time of writing. Whereas definitely not lots (the “text-generation-inference” tag yields 125,950 outcomes), time collection forecasting with basis fashions is an attention-grabbing sufficient area of interest for giant firms like Amazon, IBM and Salesforce to have developed their very own fashions: Chronos, TinyTimeMixer and Moirai, respectively. On the time of writing, probably the most fashionable 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 “sturdy zero-shot generalization capabilities” on quite a lot of datasets throughout totally different domains. As soon as fine-tuned for particular duties, in addition they declare it to be the most effective general-purpose mannequin of its sort. 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 collection knowledge. Gradient boosting algorithms corresponding to 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]. Subsequently, 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’s not that easy.
By the way in which, I can’t go into the main points 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 exploit for this train is a 4-year-long collection of hourly wave heights off the coast of Ribadesella, a city within the Spanish area of Asturias. The collection is on the market on the Spanish ports authority knowledge portal. The measurements had been taken at a station positioned within the coordinates (43.5, -5.083), from 18/06/2020 00:00 to 18/06/2024 23:00 [3]. I’ve determined to combination the collection to a day by day stage, 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 change into very unstable in a short time. Subsequently, our goal variable is the utmost top of the waves recorded in a day, measured in meters.
There are a number of the explanation why I selected this collection: the primary one is that the Lag-Llama mannequin was educated on some weather-related knowledge, though not lots, comparatively. I might count on the mannequin to search out any such knowledge barely difficult, however nonetheless manageable. The second is that, whereas meteorological forecasts are usually 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 believe statistical fashions can inform us what we might usually count on, and the way far off it’s from what is definitely occurring.
The dataset is fairly commonplace and doesn’t require a lot preprocessing aside from imputing a couple of lacking values. The plot beneath reveals what it seems like after we cut up it into prepare, 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 educated for the latter, so we should always concentrate on that one. Whereas that’s true, I consider that people discover it simpler to grasp a single quantity than a confidence interval, so I believe the purpose forecast remains to be helpful, even when only for illustrative functions.
There are lots of elements that we have to take into account when producing a forecast. A number of the most essential embody the forecast horizon, the final remark(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. Which means that 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, comparable to the dates that it simply predicted, and it produces 7 extra forecasts. The mannequin, nonetheless, just isn’t retrained as new knowledge is on the market. When it comes to our dataset, which means that we’ll produce a forecast of most wave heights for every day of the following week.
For level forecasting, we’re going to use the Imply Absolute Error (MAE) as efficiency metric. Within the case of probabilistic forecasting, we’ll purpose for empirical protection or protection chance of 80%.
The scene is about. Let’s get our arms soiled with the experiments!
Whereas initially not designed for time collection forecasting, gradient boosting algorithms generally, and XGBoost particularly, could be nice predictors. We simply have to feed the algorithm the information in the precise format. For example, if we wish to use three lags of our goal collection, we will merely create three columns (say, in a pandas dataframe) with the lagged values and voilà! An XGBoost forecaster. Nonetheless, this course of can shortly change into onerous, particularly if we intend to make use of many lags. Fortunately for us, the library Skforecast [4] can do that. Actually, Skforecast is the one-stop store for creating and testing all kinds of forecasters. I actually can’t advocate it sufficient!
Making a forecaster with Skforecast is fairly easy. We simply have to create a ForecasterAutoreg object with an XGBoost regressor, which we will then fine-tune. On high of the XGBoost hyperparamters that we might usually optimise for, we additionally have to seek for the most effective variety of lags to incorporate in our mannequin. To do this, Skforecast gives a Bayesian optimisation methodology 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 following:
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 take a look at how effectively the XGBoost forecaster does at predicting the following 7 days of most wave heights. The chart beneath 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 good.
To create the predictions depicted above, we’ve used Skforecast’s backtesting_forecaster perform, which permits us to judge the mannequin on a check set, as proven within the following code snippet. On high of the predictions, we additionally get a efficiency metric, which in our case is the MAE.
Our mannequin’s MAE is 0.64. Which means that, 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. Subsequently, our mannequin’s common error is about 0.74 items of the usual deviation. Moreover, if we had been to easily use the earlier equal remark 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, it appears that evidently, up to now, our mannequin is best 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 gives two strategies: utilizing both bootstrapped residuals or quantile regression. The outcomes usually are not very totally different, so I’m going to focus right here on the bootstrapped residuals methodology. You may see extra ends in half 3 of this pocket book.
The concept of establishing prediction intervals utilizing bootstrapped residuals is that we will randomly take a mannequin’s forecast errors (residuals) an add them to the identical mannequin’s forecasts. By repeating the method various instances, we will assemble an equal variety of various forecasts. These predictions comply with a distribution that we will 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 potential forecasts. On this universe, we might count on to see no less than a share of the particular values of the forecasted collection. In our case, we’ll purpose 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 beneath (the primary one corresponds to the code snippet within the earlier part). Strains 14-17 are the parameters that govern our bootstrap calculation.
The ensuing prediction intervals are depicted within the chart beneath.
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 massive. Consider it this fashion: if we mentioned that tomorrow’s waves can be between 0 and infinity meters excessive, we might all the time be proper, however the forecast can be ineffective! To get a concept of how massive our intervals are, Skforecast’s docs counsel that we compute the realm 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 may assist us examine throughout forecasters. In our case, the realm 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 think about within the forecast. We simply have to name the get_llama_predictions perform beneath:
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 counsel 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 beneath, 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 a degree forecast. If you have to be taught extra concerning the output of the mannequin, I counsel you take a look on the writer’s tutorial talked about above.
The authors of the mannequin advise that totally different datasets and forecasting duties might require differen context lenghts. In our case, we strive context lenghts of 32, 64 and 128 tokens (lags). The chart beneath reveals the outcomes of the 64-token mannequin.
Level forecasting
As we mentioned above, Lag-Llama just isn’t meant to calculate level forecasts, however we will get one by taking the median of the probabilistic interval that it returns. One other potential level forecast can be the imply, though it might be topic to outliers within the interval. In any case, for our specific dataset, each choices yield related 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 increased than the XGBoost forecaster’s, which went right down to 0.64. Actually, 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 commonplace. 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 all the time be the case — a really slender interval might all the time be proper. Nonetheless, in apply this trade-off may be very a lot current in all of the fashions I’ve educated.
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 characterize the elevated uncertainty as we transfer away from the final remark that the mannequin noticed. In different phrases, a forecast for the following day can be much less unsure than a forecast for the day after subsequent, and so forth.
The 128-token mannequin yields very related outcomes to the XGBoost forecaster, which had an space 348.28 and a protection of 84.67%. Primarily based on these outcomes, we will say that, with no coaching, Lag-Llama’s efficiency is moderately strong 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 advocate tuning the context size and the training fee. We’re going to discover a number of the recommended values for these hyperparameters. The code snippet beneath, which I’ve taken and modified from the authors’ fine-tuning tutorial pocket book, reveals how we will 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 very good mannequin ought to have a Protection[0.8] of round 80%. MAE Protection, however, measures the deviation of the particular protection chances from the nominal protection ranges. Subsequently, a very good mannequin in our case must be one with a small MAE and coverages of round 80% and 90%, respectively.
One of many important 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 every one fashions that I educated ended up overfitting the coaching knowledge. Alternatively, with a validation set most fashions had been optimised in Epoch 0 and didn’t enhance the validation loss thereafter. With extra knowledge, we may even see much less excessive outcomes.
As soon as educated, a lot of the fashions within the loop yield a MAE of 0.5 and coverages of 1 on the check set. Which means that the fashions have very broad prediction intervals, however the prediction just isn’t very exact. The mannequin that strikes a greater stability 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 probably the most promising mannequin, we’re going to run it by way of the checks that we’ve with the opposite forecasters.
The chart beneath reveals 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. Actually, the interval space is 188.69. With these prediction intervals, the mannequin reaches a protection of 56.67% over the 7-day recursive forecast. Do not forget 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 just too removed from the 80% protection that we’re aiming for, whereas the zero-shot mannequin with 128 tokens wasn’t.
With regards 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.
General, the fine-tuned mannequin leaves doesn’t go away us a very good image: it doesn’t do higher than a zero-shot higher at both level of probabilistic forecasting. The authors do counsel that the mannequin can enhance if fine-tuned with extra knowledge, so it might be that our coaching set was not giant sufficient.
To recap, let’s ask once more the query that we set out in the beginning of this weblog: Is Lag-Llama higher at forecasting than XGBoost? For our dataset, the brief reply is not any, they’re related. The lengthy reply is extra sophisticated, although. Zero-shot forecasts with a 128-token context size had been on the identical stage as XGBoost when it comes to probabilistic forecasting. Positive-tuning Lag-Llama additional diminished the prediction space, making the mannequin’s appropriate forecasts extra exact, albeit at a considerable price when it comes to 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 will’t say that Lag-Llama beat XGBoost.
These outcomes inevitably open a broader debate: since one just isn’t higher than the opposite when it comes to efficiency, which one ought to we use? On this case, we’d want to think about different variables corresponding to 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 consider me! The code that I used is publicly out there on this Github repo, so go take a look and run it your self.
