Monte Carlo Positive-Unlabeled Two-Step Learning for Landslide Susceptibility Mapping under Inventory Uncertainty: Comparison with Hard-Threshold PU Two-Step and EIV in Northern Morocco

In the rugged, rain-swept mountains of northern Morocco, the ground is a living, shifting entity. Steep slopes, complex geology, and heavy seasonal rains combine to make landslides a frequent and dangerous reality. For planners and safety officials, the goal is to draw a map that shows where the earth is likely to give way again. This is not a matter of guessing; it is a statistical challenge. To build a model that predicts where landslides might happen, scientists need two things: a list of places where landslides have already occurred, and a list of places where the ground is stable. The first list is easy to find; the second is a trap. Just because a landslide has not been recorded in a specific spot does not mean the ground is safe. It might simply mean the landslide was missed, hidden by vegetation, or too old to be seen. Treating these unrecorded spots as confirmed "safe" zones is like assuming a room is empty because you didn't see anyone inside, ignoring the possibility that someone is hiding in the closet. This uncertainty makes it incredibly difficult to teach a computer to distinguish between stable ground and ground that is merely waiting to slide.

A team of researchers from Morocco has tackled this problem by developing a new way to handle these "missing" landslides. Instead of forcing a computer to make a single, rigid decision about which unrecorded spots are safe, they created a method that embraces uncertainty. They tested this new approach, called MC-PU-2S, against two existing methods in the Rif mountains, an area known for its steep terrain and frequent slope failures. The study used a database of nearly 6,000 observations, including over 2,300 known landslide locations and thousands of other points where the ground status was unknown. By running their models through a rigorous testing process that prevented the computer from overfitting by memorizing the test data, the researchers found that their new method produced a much clearer and more reliable picture of risk. While the older methods tended to label almost the entire landscape as dangerous, blurring the lines between high risk and low risk, the new approach successfully separated the two, offering not just a map of danger, but a map of confidence.

The core of the problem lies in how traditional models handle the "negative" class—the spots assumed to be safe. In many studies, researchers simply pick random spots away from known landslides and tell the computer, "This is safe." The new study argues that this is a flawed assumption. If a spot is actually unstable but just hasn't been mapped yet, the computer learns the wrong lesson. The researchers compared three different strategies for handling this. The first, known as the Enhanced Information Value method, tries to filter out the safest spots by looking at a preliminary model and picking the very lowest-risk areas. The second, called PU Two-Step, uses a strict cutoff point: if a spot looks safe enough according to a specific score, it is labeled safe; if it is even slightly less safe, it is discarded. Both of these methods force a binary choice, creating a sharp line between safe and unsafe that may not exist in the real world.

The researchers' new method, MC-PU-2S, takes a different path. Instead of drawing a hard line, it assigns a probability to every unknown spot. It asks, "How likely is it that this spot is truly safe?" and allows the answer to be a shade of gray rather than black or white. To do this, the computer runs hundreds of simulations. In each simulation, it randomly decides whether to treat a specific unknown spot as safe or unsafe, based on that probability. It then builds a prediction model for each of these scenarios. Finally, it averages all these hundreds of models together. This process smooths out the errors and reveals which predictions are solid and which are shaky. The result is not just one map of susceptibility, but a suite of products: a map showing the average risk, a map showing how much the prediction varies across the simulations, and a map highlighting areas where the model simply cannot decide.

When the researchers compared the results, the difference was striking. The older methods produced maps where almost every single point in the study area was classified as having a high risk of landslides. The computer was essentially shouting "danger" everywhere, which is not helpful for planning. The new method, however, produced a much more balanced view. It correctly identified that while many areas are indeed risky, a significant portion of the landscape is stable. The new model was far better at distinguishing between the two, with its predictions aligning much more closely with the actual data. It also fixed a major flaw in the older models: their probability estimates were compressed and biased, meaning they could not accurately tell an AUC of 0.9 from an AUC of 0.6. The new method spread these probabilities out, allowing for a more nuanced understanding of the terrain.

Perhaps the most valuable output of this new approach is the ability to identify uncertainty. The study found that in about 23 percent of the area, the model could not confidently say whether the ground was safe or unsafe. These are the spots where the classification hovers right on the edge of the decision line. In a traditional map, these areas would look just like the rest, hiding a critical lack of knowledge. In the new maps, these areas are flagged explicitly. This is a game-changer for decision-makers. A high-risk area with high confidence can be immediately targeted for safety measures. A high-risk area with low confidence signals that more fieldwork is needed before any money is spent on construction or mitigation. It tells officials exactly where to look next, turning a vague warning into a specific action plan.

The study also confirmed that the most important factors driving landslides in this region remain consistent with what geologists already know: the steepness of the slope, the distance to roads, the type of rock, and the amount of rainfall. However, the way these factors are interpreted changes when the uncertainty is accounted for. The new method showed that the relationship between these factors and the risk is not a simple switch but a complex gradient. By averaging out the noise of the "missing" landslides, the model could see these patterns more clearly. The researchers noted that while their method requires more computing power than the older techniques, the trade-off is worth it. The ability to quantify uncertainty and produce a map that admits what it does not know is a significant step forward in managing natural hazards.

This work does not claim to have solved the problem of landslide prediction entirely. The researchers are careful to note that their method is sensitive to the quality of the initial data and that the number of simulations used in their study was a pilot test. They suggest that future work should run even more simulations to ensure the results are stable. They also point out that their method only measures one type of uncertainty: the uncertainty about which spots are truly safe. It does not account for errors in the maps themselves or changes in the weather over time. Nevertheless, the study demonstrates that moving away from rigid, black-and-white thinking toward a probabilistic approach yields better results. In a world where the ground is constantly shifting, a model that can admit its own doubts is far more useful than one that is confidently wrong. The new maps from northern Morocco offer a clearer, more honest guide for protecting communities living on the edge of the slope.