Jonne Pohjankukka

Jonne Pohjankukka, Jukka Heikkonen

This work addresses the problem of variance in stochastic gradient estimation for machine learning optimization. Deep learning relies on mini-batch methods such as stochastic gradient descent, which approximate full gradients but introduce noise, creating trade-offs between convergence stability, speed, and generalization. Existing methods, including variance reduction techniques (e.g., SVRG and SAG) and adaptive optimizers, aim to mitigate gradient noise but may introduce additional computational overhead. We propose a model-assisted sampling framework that interprets mini-batch gradients through survey sampling theory, treating the dataset as a fixed finite population and gradients as sample-based estimates. Our aim is to bridge machine learning optimization and survey sampling theory by combining their perspectives on sample-based estimation and variance reduction. By incorporating auxiliary gradient-prediction models, we construct more efficient gradient estimators, with uniform sampling arising as a special case when no auxiliary information is used. Our approach integrates easily with existing optimizers, improving efficiency without altering their dynamics. Empirical results on synthetic and six benchmark datasets show performance gains in 71-86% of the experiments, particularly for medium-sized input spaces in our benchmarks. Notably, with momentum-based optimizers such as AdamW, the proposed estimator achieves clearly better generalization in roughly half the training epochs compared to baseline estimator.

Jonne Pohjankukka, Sakari Tuominen, Jukka Heikkonen

In large-area forest inventories a trade-off between the amount of data to be sampled and the costs of collecting the data is necessary. It is not always possible to have a very large data sample when dealing with sampling-based inventories. It is therefore necessary to optimize the sampling design in order to achieve optimal population parameter estimation. On the contrary, the availability of remote sensing (RS) data correlated with the forest inventory variables is usually much higher. The combination of RS and the sampled field measurement data is often used for improving the forest inventory parameter estimation. In addition, it is also reasonable to study the utilization of RS data in inventory sampling, which can further improve the estimation of forest variables. In this study, we propose a data sampling method based on Bayesian optimization which uses RS data in forest inventory sample selection. The presented method applies the learned functional relationship between the RS and inventory data in new sampling decisions. We evaluate our method by conducting simulated sampling experiments with both synthetic data and measured data from the Aland region in Finland. The proposed method is benchmarked against two baseline methods: simple random sampling and the local pivotal method. The results of the simulated experiments show the best results in terms of MSE values for the proposed method when the functional relationship between RS and inventory data is correctly learned from the available training data.

Jonne Pohjankukka, Tapio Pahikkala, Paavo Nevalainen et al.

In machine learning one often assumes the data are independent when evaluating model performance. However, this rarely holds in practise. Geographic information data sets are an example where the data points have stronger dependencies among each other the closer they are geographically. This phenomenon known as spatial autocorrelation (SAC) causes the standard cross validation (CV) methods to produce optimistically biased prediction performance estimates for spatial models, which can result in increased costs and accidents in practical applications. To overcome this problem we propose a modified version of the CV method called spatial k-fold cross validation (SKCV), which provides a useful estimate for model prediction performance without optimistic bias due to SAC. We test SKCV with three real world cases involving open natural data showing that the estimates produced by the ordinary CV are up to 40% more optimistic than those of SKCV. Both regression and classification cases are considered in our experiments. In addition, we will show how the SKCV method can be applied as a criterion for selecting data sampling density for new research area.