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Accepted as a paper at ICLR 2023 Workshop on Machine Learning for Remote Sensing

EVALUATION CHALLENGES FOR GEOSPATIAL ML

Esther Rolf

Harvard University

ABSTRACT

As geospatial machine learning models and maps derived from their predictions

are increasingly used for downstream analyses in science and policy, it is im-

perative to evaluate their accuracy and applicability. Geospatial machine learn-

ing has key distinctions from other learning paradigms, and as such, the correct

way to measure performance of spatial machine learning outputs has been a topic

of debate. In this paper, I delineate unique challenges of model evaluation for

geospatial machine learning with global or remotely sensed datasets, culminating

in concrete takeaways to improve evaluations of geospatial model performance.

1 M OTIVATION

Geospatial machine learning (ML), for example with remotely sensed data, is being used across

consequential domains, including public health (Nilsen et al., 2021; Draidi Areed et al., 2022) con-

servation (Sofaer et al., 2019), food security (Nakalembe, 2018), and wealth estimation (Jean et al.,

2016; Chi et al., 2022). By both their use and their very nature, geospatial predictions have a purpose

beyond model benchmarking; mapped data are to be read, scrutinized, and acted upon. Thus, it is

critical to rigorously and comprehensively evaluate how well a predicted map represents the state of

the world it is meant to reflect, or how well a spatial ML model performs across the many conditions

in which it might be used.

Unique structures in remotely sensed and geospatial data complicate or even invalidate use of tradi-

tional ML evaluation procedures. Partially as a result of misunderstandings of these complications,

the stated performance of several geospatial models and predictive maps has come into question

(Fourcade et al., 2018; Ploton et al., 2020). This in turn has sparked disagreement on what the

“right” evaluation procedure is. With respect to a certain set of spatial evaluation methods (described

in §4.1), one is jointly presented with the arguments that “spatial cross-validation is essential in pre-

venting overoptimistic model performance” (Meyer et al., 2019) and “spatial cross-validation meth-

ods have no theoretical underpinning and should not be used for assessing map accuracy” (Wadoux

et al., 2021). That both statements can simultaneously hold reflects the importance of using a diverse

set of evaluation methods tailored to the many ways in which a geospatial ML model might be used.

In this paper, I situate the challenges of geopsatial model evaluation in the perspective of an ML

researcher, synthesizing prior work across ecology, geology, statistics, and machine learning. I aim

in part to disentangle key factors that complicate effective evaluation of model and map performance.

First and foremost, evaluation procedures should be designed to measure as closely as possible the

quantity or phenomena they are intended to assess (§2). After the relevant performance measures

are established, considerations can be made about what is feasible with the available data (§3). With

all of this in mind, possible evaluation procedures (§4) can be compared and tailored to the task at

hand. Recognizing the interaction of these distinct but related steps exposes opportunities to improve

geospatial performance assessment, both in individual studies and more broadly (§5).

2 M AP ACCURACY AND MODEL PERFORMANCE : CONTRASTING VIEWS

Estimating accuracy indices and corresponding uncertainties of geospatial predictions is essential

to reporting geospatial ML performance (§2.1), especially when prediction maps will be used for

downstream analyses or policy decisions. At the same time, the potential value of a geospatial ML

model likely extends beyond that of a single mapped output (§2.2). Delineating the (possibly many)

facets of desired model and map use is key to measuring geospatial ML performance (§2.3).

1arXiv:2303.18087v1 [cs.LG] 31 Mar 2023

Accepted as a paper at ICLR 2023 Workshop on Machine Learning for Remote Sensing

2.1 M AP ACCURACY AS A POPULATION PARAMETER TO BE ESTIMATED

Establishing notation we will use throughout, let ˆy(ℓ)denote a model’s predicted value at location

ℓ, andy(ℓ)the reference, or “ground truth” value (which we assume can be measured). To calculate

amap accuracy index as a population parameter for accuracy index Fis to calculate A(D) =

F({(ˆy(ℓ),y(ℓ))}ℓ∈D)whereDis the target population of map use (e.g. all (lat, lon) pairs in a

global grid, or all administrative units in a set of countries). Examples of common Finclude root

mean squared error, and area under the ROC curve, among many others (Maxwell et al., 2021).

Typically, one only has a limited set of values yfor locations in an evaluation set ℓ∈S evalfrom which

to compute a statistic ˆA(Seval)to estimateA(D). Wadoux et al. (2021) discuss the value of using a

design-independent probability sample for design-based estimation of A(in contrast, model-based

estimation makes statistical assumptions about the data (Brus, 2021)). Here a design-independent

sample is one collected independently of the model training process. A probability sample is one

for which every location in Dhas a positive probability of appearing in Seval, and these probabilities

are known for all ℓ∈S eval(see, e.g. Lohr (2021)). Wadoux et al. (2021) emphasize that when Seval

is a design independent probability sample from population D, design-based inference can be used

to estimateA(D)with ˆA(Seval),regardless of the prediction model or distribution of training data .

Computing statistically valid estimates of map accuracy indices is clearly a key component of re-

porting overall geospatial ML model performance. It is often important to understand how accuracy

and uncertainty in predictions vary across sub-populations Dr1,Dr2...⊂D (such as administrative

regions or climate zones (Meyer & Pebesma, 2022)). If local accuracy indexesA(Dr1),A(Dr2)...

are low in certain sub-regions, this could expose concerns about fairness or model applicability.

2.2 M ODEL PERFORMANCE EXTENDS BEYOND MAP ACCURACY

Increasingly, geospatial ML models are designed with the goal of being used outside of the regions

where training labels are available. Models trained with globally available remotely sensed data

might be used to “fill in” spatial gaps common to other data modalities (§3.2). The goals of spatial

generalization ,spatial extrapolation orspatial domain adaption can take different forms: e.g.

applying a model trained with data from one region to a wholly new region, or using data from a few

clusters or subregions to extend predictions across the entire region. When spatial generalizability

is desired, performance should be assessed specifically with respect to this goal (§4).

While spatial generalization is a key component of performance for many geospatial models, it too

is just one facet of geospatial model performance. Proposed uses of geospatial ML models and

their outputs include estimation of natural or causal parameters (Proctor et al., 2023), and reducing

autocorrelation of prediction residuals in-sample (Song & Kim, 2022). Other important facets of

geospatial ML performance are model interpretability (Brenning, 2022) and usability, including the

resources required to train, deploy and maintain models (Rolf et al., 2021).

2.3 C ONTRASTING PERSPECTIVES ON PERFORMANCE ASSESSMENT

The differences between estimating map accuracy as a population parameter (§2.1) and assessing a

model’s performance in the conditions it is most likely to be used (§2.2) are central to one of the

discrepancies introduced in §1. Meyer et al. (2019); Ploton et al. (2020); Meyer & Pebesma (2022)

state concerns in light of numerous ecological studies applying non-spatial validation techniques

with the explicit purpose of spatial generalization. They rightly caution that when data exhibit spa-

tial correlation (§3.1), non-spatial validation methods will almost certainly over-estimate predictive

performance in these use cases. Wadoux et al. (2021), in turn, argue that performance metrics from

spatial validation methods will not necessarily tell you anything about Aas a population parameter.

A second discrepancy between these two perspectives hinges on what data is assumed to be avail-

able (or collectable). While there are some major instances of probability samples being collected

for evaluation of global-scale maps (Boschetti et al., 2016; Stehman et al., 2021), this is far from

standard standard in geospatial ML studies (Maxwell et al., 2021). More often, datasets are created

“by merging all data available from different sources” (Meyer & Pebesma, 2022). Whatever the

intended use of a geospatial model, the availability of and structures within geopsatial and remotely

sensed data must be contended with in order to reliably evaluate any sort of performance.