ICAR-IASRI MSc and PhD (Agricultural Statistics, Computer Application, Bioinformatics) · India · ICAR-Indian Agricultural Statistics Research Institute with the IARI Graduate School
Original practice questions written to the published syllabus · not past papersPrediction from data with honest validation: the bias-variance trade-off, regularised regression, trees and ensembles, support vector machines, neural networks and deep learning for images, unsupervised learning, and how to use them on yield, disease, price and image data without fooling yourself. The Agribusiness and Agricultural Engineering tracks introduce ML; this is the statistician's full course.
In the exams: GATE DA 'Machine Learning' and 'AI' (heavy); AICE-JRF Computer Application (present); SAS Statistics for Machine Learning credential (present)
ICAR-IASRI MSc and PhD programmes (Agricultural Statistics, Computer Application)
Statistical learning with agricultural data: penalised regression and genomic prediction, ensembles and SVMs for yield and remote sensing, CNNs for plant images, and blocked validation.
How our questions for ICAR-IASRI MSc and PhD spread across the units of Statistical & Machine Learning for Agriculture. Difficulty: 26 easy, 52 medium, 16 hard.
| Neural networks and deep learning; CNNs for plant and field images | 10 | |
| Cross-validation: k-fold and leave-one-out; spatial and temporal blocking | 9 | |
| Regularised regression: ridge, lasso and elastic net | 9 | |
| Linear and quadratic discriminant analysis and logistic classification | 9 | |
| Decision trees, random forests and gradient boosting | 9 | |
| Supervised learning and the bias-variance trade-off | 8 | |
| k-nearest neighbours and naive Bayes | 8 | |
| Support vector machines | 8 | |
| Unsupervised learning: k-means, k-medoids and hierarchical clustering | 8 | |
| Dimensionality reduction: PCA and embeddings | 8 | |
| Model interpretation: variable importance and SHAP | 8 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
With 3 classes and 10 predictors, how many covariance parameters must QDA estimate in total?
C. 165
Each 10 x 10 covariance matrix has p(p + 1)/2 = 55 distinct parameters, and QDA needs one per class: 3 x 55 = 165. LDA needs only 55; 300 ignores symmetry; 30 counts variances only.
Further reading: James et al., An Introduction to Statistical Learning
For a node with 30 diseased and 70 healthy plants, what is the entropy in bits?
D. 0.881
Entropy = -(0.3 log2 0.3 + 0.7 log2 0.7) = 0.881 bits. Natural logs give 0.611 nats; 1.000 is the maximum, for a 50:50 node.
Further reading: Breiman (2001); Hastie, Tibshirani and Friedman, The Elements of Statistical Learning
In bagging with n = 100 observations, what proportion of observations is expected to be left out of a given bootstrap sample?
C. 0.366
Each observation is missed with probability (1 - 1/100)^100 = 0.366, close to 1/e = 0.368. 0.632 is the proportion included; these out-of-bag cases give a free test-error estimate.
Further reading: Breiman (2001); Hastie, Tibshirani and Friedman, The Elements of Statistical Learning
How does a random forest differ from bagged trees?
B. Each split considers only a random subset of predictors
Random predictor subsets decorrelate the trees, so averaging reduces variance more; fitting residuals sequentially is boosting.
Further reading: Breiman (2001); Hastie, Tibshirani and Friedman, The Elements of Statistical Learning
What is the main weakness of a single, unpruned decision tree?
A. High variance
Small changes in data can change the whole tree, so its predictions vary greatly; trees model interactions and handle categorical predictors naturally.
Further reading: Breiman (2001); Hastie, Tibshirani and Friedman, The Elements of Statistical Learning
How many parameters (weights plus biases) does a fully connected layer from 100 inputs to 50 units have?
C. 5,050
100 x 50 = 5,000 weights plus 50 biases = 5,050. 5,000 omits biases; 5,100 counts 100 biases.
Further reading: Goodfellow, Bengio and Courville, Deep Learning
Which linkage in hierarchical clustering tends to produce long, straggly chains of clusters?
C. Single linkage
Single linkage merges on the closest pair, so clusters can grow by chaining; complete linkage and Ward's method produce compact clusters.
Further reading: James et al., An Introduction to Statistical Learning; Kaufman and Rousseeuw
What is a medoid?
B. A real observation central to its cluster
k-medoids represents each cluster by a real case, which is robust to outliers and easy to describe.
Further reading: James et al., An Introduction to Statistical Learning; Kaufman and Rousseeuw
By the eigenvalue-greater-than-one rule, how many components would be kept from a correlation-matrix PCA with eigenvalues 2.4, 1.1, 0.3 and 0.2?
A. 2
Two eigenvalues (2.4 and 1.1) exceed 1, the average eigenvalue of a correlation matrix.
Further reading: James et al., An Introduction to Statistical Learning
A yield model's most important predictor by SHAP is the field identifier. What should the analyst suspect?
A. It memorises fixed field-level effects
Identifiers carry fixed field effects; a model relying on them will not generalise to new fields. Interpretation is a check for such artefacts.
Further reading: Molnar, Interpretable Machine Learning; Lundberg and Lee (2017)
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