Syllabus
Course purpose, weekly plan, assessment, and policies
Course purpose
The course connects mathematical foundations with modern machine-learning practice. Students will learn to formulate learning problems, evaluate evidence, compare models, and communicate the limitations of an analysis.
Learning objectives
By the end of the course, students should be able to:
- distinguish prediction, estimation, and decision-making goals;
- construct and justify training, validation, and test procedures;
- explain the assumptions behind representative supervised-learning methods;
- diagnose overfitting, leakage, misspecification, and misleading metrics;
- design reproducible experiments and interpret results in context.
Weekly plan
Lectures develop fundamentals; tutorials bridge them to practice through worked investigations and stories. The readings identify relevant topics rather than whole-book assignments. Optional extensions are labeled explicitly. Yandex Handbook readings are in Russian; this syllabus and the other listed books are in English.
Course materials are available on the Lectures, Tutorials, Textbook and Labs pages. Dates and assignment instructions are published separately.
| Week # | Lecture | Tutorial | Lab |
|---|---|---|---|
| 1 | Machine learning through the simplest complete model ML paradigms; Mitchell’s Experience–Task–Performance measure view of learning; features, targets, predictions, parameters, and hyperparameters; stages of an ML project; train/validation/test data; linear regression in matrix form; MSE loss; gradient descent numerical intuition. Parameters are fitted to data; hyperparameters and representations are selected using validation. Distinguish fitting, model selection and final evaluation. Scope: MSE is introduced as a fitting objective; Gaussian likelihood and its MSE derivation are studied in Week 07. Reading: Bishop, PRML: linear models for regression (least squares); Yandex: linear models. Read the fitting objective; defer probabilistic derivations to Week 07. |
A Story of 3 and 7 Follow handwritten-digit recognition from a mean-image classifier and handcrafted features to frozen CNN embeddings and joint image–text embeddings; compare kNN decisions and PCA visualizations. Connect the changing representation to what a simple classifier can learn. Calculate regression predictions, residuals and one simultaneous gradient update; explain why a lower training loss alone is insufficient. Materials: Week 01 lecture resources, tutorial page. |
Linear regression from scratch Lab 1 |
| 2 | Classification: logistic regression, SVMs and kernels Training-data EDA; feature scaling, nominal/ordinal encoding and preprocessing; logits, sigmoid and log-odds; learned decision boundaries and polynomial feature maps; BCE as a fitting loss; decision thresholds, confusion matrices, precision, recall, F1 and ROC/PR trade-offs; one-vs-rest, softmax and multiclass cross-entropy. Distinguish model scores, probabilities and decisions. Scope: Introduce and interpret BCE/CE here; Bernoulli/categorical likelihood derivations and information theory are studied in Week 07. Self-study — SVMs and kernels: margins and support vectors; soft margins, hinge loss and C; linear, polynomial and RBF kernels as implicit feature maps; scaling, gamma and validation-based selection. Distinguish decision scores from calibrated probabilities. Full dual/KKT derivations are optional. Reading: Bishop, PRML: linear models for classification; Prince, Understanding Deep Learning: supervised learning and loss functions. Focus on logits, predictions and loss use; defer likelihood derivations to Week 07. Bishop, PRML: kernel methods and sparse kernel methods. |
Drawing the Line: from data to decisions Follow two moons and Iris through EDA, scaling, encoding, linear/polynomial boundaries, scores, probabilities and thresholds. Change the threshold without retraining; compare classification errors and validation metrics. Explain numerical stability and the expected inputs of BCEWithLogitsLoss and CrossEntropyLoss. Likelihood, entropy and KL sections in the existing notebook are readings for Week 07.Materials: Week 02 lecture resources, tutorial page. SVM bridge: compare a logistic boundary with linear/RBF SVM boundaries; examine scaling, C and gamma. Use the SVM guide for independent practice before the Week 03 lab. |
EDA and logistic regression Lab 2 |
| 3 | Decision trees CART for classification and regression; recursive partitioning and prediction paths; weighted split criteria, Gini impurity and entropy; greedy growth, pruning, depth/leaf-size controls and overfitting. Introduce the bias–variance motivation for combining models; ensemble construction is developed in the tutorial. Reading: Yandex: decision trees; Yandex: ensembles. |
From one unstable tree to a useful ensemble Bias–variance trade-off, bootstrap/bagging, out-of-bag evaluation, random forests and ensemble diversity; additive models, stage-wise/functional optimization, gradient boosting, residuals and shrinkage. Compare XGBoost, LightGBM and CatBoost, including missing/categorical data. Practice cross-validation, random/Bayesian hyperparameter search, leakage control and avoiding leaderboard overfitting. TabPFN/TabICL-style tabular foundation models are an optional comparison. Week 02 SVM connection: compare scaled SVM/kernel baselines with tree methods in the existing lab. The instructor reports the best class results came from SVMs; investigate the task-specific explanation. Materials: trees lecture, ensembles tutorial (presentations in Russian); SVM guide. |
Private tabular-data competition Hidden Pairs |
| 4 | Nonlinear representation learning with feedforward neural networks Learned representations; artificial neurons as affine transformations followed by activations; why depth needs nonlinearity; layers, tensor shapes, and MLP forward propagation; task-dependent outputs, logits, Softmax, and cross-entropy; scalar computation graphs and the chain rule; matrix backpropagation and PyTorch autograd; the training loop, mini-batches, learning rate, optimizer state, initialization, validation, regularization, and generalization. Reading: Prince: shallow/deep networks, fitting models and gradients; Goodfellow et al., Deep Learning: Ch. 6–8 (feedforward networks, regularization, optimization). |
Ode to Autograd ReLU hinges and a trained \(1\to4\to1\) network; XOR as hidden representation learning; a numerical forward-pass ledger; scalar computation graphs, local derivatives, branch addition, and ReLU gating; central finite-difference gradient checking; row-major batch notation and manual matrix backpropagation; verification against PyTorch autograd; leaf and non-leaf tensors, retain_grad(), gradient accumulation, detach(), and the distinction between backpropagation and the optimizer step.Story: from a ReLU hinge to XOR, then ask which hidden representation makes the output problem easy. Separate gradient calculation from parameter updates and optimization from generalization. Materials: lecture resources, tutorial, our Chapter 04. |
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| 5 | Visual representation learning with convolutional neural networks Images as structured data; convolution; locality and parameter sharing; padding, stride, pooling, and receptive fields; feature hierarchies; residual connections; data augmentation; transfer learning and fine-tuning; CNNs versus MLPs. Normalization and invariance assumptions; distinguish architecture, training procedure and evaluation evidence. Reading: Prince: convolutional and residual networks; Goodfellow et al.: Ch. 9, Convolutional Networks; Yandex: convolutional networks. |
Convolution, residual learning, and transfer learning Convolution from scratch; output-shape calculations; residual blocks; batch normalization; augmentation as an invariance assumption; pretrained backbone versus training from scratch; fine-tuning strategies; error analysis; brief 1D-CNN connection. Story: build a local-pattern detector, reuse it across positions, then compare an MLP and Conv1d on MNIST-1D before the satellite-image application. Calculate local responses, shared gradients and normalization axes; compare architectures under controlled conditions. Materials: lecture resources, tutorial, our Chapter 05. |
Image-classification competition Satellite scene classification |
| 6 | Sequential representation learning with RNNs and Transformers Sequences of measurements, words, and image patches; autoregression; RNNs; LSTM and GRU intuition; hidden states and vanishing gradients; attention and self-attention; Transformer encoders; tokens, embeddings, positional information, and masking. Backpropagation through time; attention scaling, encoder blocks and task heads; causal versus bidirectional information flow. Reading: Prince: Transformers; Goodfellow et al.: Ch. 10, Sequence Modeling. |
Transformer anatomy and sequence validation Small RNN implementation; backpropagation through time; attention calculation; causal versus bidirectional modeling; temporal splitting and sequence leakage; selected Attention Is All You Need analysis; Transformer encoder inspection; Vision Transformer connection and CNN-versus-ViT comparison after introducing attention and image-patch tokens. Story: a robot must remember a delayed command; follow the information through recurrent memory, gates and attention. Trace one recurrent gradient and one attention row, compare held-out recall across initializations, and identify what each prediction may access. Continuous-wave forecasting leads into Week 09. Materials: lecture resources, tutorial, our Chapter 06. |
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| 7 | Frequentist and Bayesian approaches; an introduction to latent-variable models Probability, conditional models and likelihood; MLE, MAP, priors, evidence, posterior and predictive distributions; frequentist versus Bayesian interpretations; Gaussian → MSE, Bernoulli → BCE and categorical → CE; entropy, cross-entropy and KL, including their decomposition and the connection between MAP and regularization. Optional maximum-entropy interpretation. VAE idea and Bayes’ theorem: distinguish a generative model from inference about latent causes of an observed image. Explain prior, likelihood, evidence and latent posterior; introduce the encoder as an approximation to Bayesian inference and the decoder as the generative direction. Inspect reconstruction, interpolation and sampling conceptually. VAE loss, ELBO, reparameterization mathematics and optimization are studied in Week 10. Reading: Bishop, PRML: probability, Bayesian linear regression and approximate inference; Goodfellow et al.: Ch. 3, Probability and Information Theory. |
Learning from evidence, then asking what generated an image Follow noisy measured data from a fitted line to a Bayesian posterior and predictive distribution; identify the roles of prior, likelihood and evidence and compare a point estimate with posterior inference. Then use VAE reconstructions, interpolations and generated images to connect latent-variable inference to Bayes’ theorem. Keep this VAE story conceptual; loss calculations and the ELBO are studied in Week 10. Materials: lecture resources, tutorials, textbook. Use the relevant Bayesian and conceptual VAE sections; later-method sections in the existing resources are forward reading. |
Uncertainty estimation — CIFAR-10N |
| 8 | Midterm examination — 90 minutes Scope: Weeks 01–07 topics in this syllabus, including Week 02 SVM/kernel self-study and the conceptual VAE introduction. VAE loss and related mathematics are studied in Week 10. The published example declares the examination structure and provides practice questions with answers. Review: study the recommended books listed in Weeks 01–07 and our lecture slides, textbook and tutorials. |
No tutorial | No lab |
| 9 | Signal processing and machine learning Sampled signals, sampling rate and aliasing; time-domain statistics, filtering and normalization; windows, discrete Fourier analysis, power spectra and short-time Fourier spectrograms; time–frequency resolution. Wavelets as localized, multiscale representations: scale/translation, continuous-wavelet scalograms and discrete-wavelet/filter-bank intuition. Compare stationary frequency content with transient events. Learning from signals: handcrafted temporal/spectral/wavelet features, 1D CNNs, recurrent models and Transformers; connect self-supervised signal representations to Week 11 and preview predictive uncertainty studied in Week 12. Complex wavelet theory is optional. Reading: Downey, Think DSP: signals, spectra, filtering and sampling; revisit our Chapter 06 for sequence models. PyWavelets provides the wavelet reference. Released materials: Two 90-minute lectures — interactive HTML and PDF, including EEGNet and a detailed Chronos-2 walkthrough. |
One pump, several pipelines A separate 90-minute SKAB laboratory compares robust statistics, PCA, raw and causal-window Isolation Forest, calibrated score fusion, and recorded Chronos-2 forecasts with a matched persistence baseline. Detect the whole faulty period; examine onset timing separately. Split whole runs, fit preprocessing on normal training data, calibrate on a separate normal reference and choose the alarm policy on validation only. Freeze the choice before revealing held-out runs; distinguish ranking, state coverage and false alarms. Student notebooks — EN/RU. |
SKAB · fault-state anomaly detection Lab instructions and student notebooks — EN/RU |
| 10 | Discovering Structure with Unsupervised Learning PCA as projection, variance preservation and reconstruction optimization; k-means objectives and clustering assumptions; mixture models and EM intuition; autoencoders, bottlenecks and reconstruction losses. Distinguish clustering, density modeling, reconstruction and downstream usefulness. Nonlinear visualization: t-SNE as a neighborhood-based view of high-dimensional data; compare with PCA and distinguish visual exploration from clustering or a predictive representation. UMAP is an optional comparison. VAE mathematics: latent generative model and approximate posterior; evidence and the ELBO; reconstruction and KL terms; Gaussian latent parameterization and the reparameterization trick; sampling, optimization and the effect of weighting the KL term. This develops the conceptual introduction from Week 07. Full mixture-model/EM derivations remain optional. Reading: Goodfellow et al.: Ch. 13–14, Linear Factor Models and Autoencoders; Bishop, PRML: mixtures/EM and continuous latent variables; Yandex: clustering. Detailed EM derivations are optional. For VAE derivations: Prince, Understanding Deep Learning: variational autoencoders and Goodfellow et al.: Ch. 19–20, approximate inference and deep generative models. |
Compressing an image is not the same as understanding it Compare raw features, PCA and an autoencoder on one dataset; inspect reconstruction, neighborhoods and clusters with a declared downstream evaluation protocol. Compare PCA and t-SNE plots, vary perplexity and initialization, and examine which neighborhoods are stable. Explain why apparent cluster sizes and distances between separated groups can be misleading and why a plot alone does not validate a clustering. Then revisit the Week 07 VAE: trace encoder distribution parameters, reparameterized samples and decoder outputs; calculate reconstruction/KL loss terms and connect them to the ELBO. Change bottleneck size or KL weight and interpret reconstruction versus sampling quality. Discuss posterior collapse and why low reconstruction error need not imply useful class structure. Materials: PCA guide, clustering guide, and the VAE sections of our Chapter 07 and existing tutorial. t-SNE reference. |
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| 11 | Self-supervised and multimodal representation learning Supervision from data views; metric learning, positive/negative pairs and InfoNCE; SimCLR, temperature, augmentation assumptions and representation collapse; teacher–student approaches including BYOL and the self-supervised DINO family; masked modeling and masked autoencoders (MAE). CLIP and image–text contrastive alignment; distinguish label-free image learning from paired-text supervision. Evaluation: linear probing versus fine-tuning, limited-label transfer, retrieval, pretraining-data disclosure and fair compute budgets. Detailed BYOL/DINO/MAE architecture comparisons are extensions around the central SimCLR/CLIP examples. Reading: Goodfellow et al.: Ch. 15, Representation Learning; Yandex: representation learning; SimCLR: objective and augmentations; CLIP: paired supervision and transfer. |
Recognize the same thing through two views, then find it with words Calculate a small InfoNCE loss, vary augmentation/temperature, and diagnose collapse or shortcut learning. Use face recognition/ArcFace as a metric-learning case study; connect image retrieval to CLIP text queries. Compare frozen linear probes, limited-label fine-tuning and retrieval under the same data/compute protocol. Revisit the Week 10 PCA/t-SNE tools on learned embeddings, with UMAP as an optional comparison; evaluate downstream performance as well as visual structure. Read selected SimCLR, DINO/BYOL and MAE designs to identify where their supervision comes from; disclose pretraining and evaluation data. |
Learn useful representations with limited labels |
| 12 | Dense prediction, object detection and prompted vision Segmentation: one class per pixel, semantic versus instance and panoptic outputs; encoder–decoder architectures, U-Net and skip connections; pixel-wise BCE/CE, Dice loss, IoU, class imbalance and transfer learning. Detection: classification with localization, bounding boxes and IoU; one-stage YOLO family versus two-stage detection; confidence, non-maximum suppression, precision–recall and AP; DETR, set prediction and Hungarian matching. Visual prediction and uncertainty: confidence versus correctness, label noise, calibration and predictive uncertainty under shift/OOD. Introduce aleatoric and epistemic sources using visual classification. Deep ensembles, Monte Carlo dropout, confidence/credible intervals and conformal coverage assumptions are extension readings. Foundation-model connections: build on CLIP to introduce open-vocabulary detection and visual grounding; distinguish self-supervised DINO visual features from the DINO detector and Grounding DINO. Introduce the SAM family through prompted segmentation in images/video, with language-guided combinations as a bridge from text to boxes to masks. Core derivations use U-Net and representative YOLO/DETR designs; broader family surveys are guided comparisons. Reading: our Chapter 05; U-Net paper; YOLO family documentation; DETR paper; panoptic segmentation paper. Further reading: DINOv2, Grounding DINO, SAM 2, SAM family: concept prompting. Uncertainty reading: calibration and temperature scaling; optional conformal prediction. |
From one image label to “find this object and outline it” Trace U-Net shapes and skip connections, inspect a partial implementation, and compare BCE/CE with Dice on an imbalanced mask. Compute IoU/Dice and diagnose boundary errors. Follow a YOLO prediction through boxes, scores and NMS; contrast DETR matching and duplicate handling. Compare missed objects, false positives and precision–recall/AP. CLIP-to-grounding bridge: use a text query to motivate Grounding DINO boxes and SAM-family masks; compare a self-supervised DINO feature backbone, a detector and a prompted segmenter. Inspect one image/mask example and one detection/grounding pipeline; use pretrained models for the broader comparisons. SAM 2 image/video prompting and current SAM-family language/concept prompting are guided extensions. Optional comparisons include real-time DETR-style detectors and YOLOE-style open-vocabulary detection; optional depth estimation connects dense features to 3D vision. When the model is confident but wrong: use a small visual-classification example to read reliability diagrams and ECE, fit temperature scaling using validation NLL, and compare errors with confidence under label noise or shift. Ensemble disagreement and dropout are optional follow-ups. Distinguish classification calibration from detection scores and mask quality. |
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| 13 | Physics-informed and scientific machine learning Scientific ML, surrogate models, simulators and differentiable models; physical priors and equations as supervision; forward and inverse problems in ODEs/PDEs. Physics-informed neural networks (PINNs) and inverse PINNs (iPINNs): data, equation-residual, initial and boundary losses; automatic differentiation with respect to inputs and unknown parameters; balancing losses, identifiability, optimization failure modes and limitations. Outlook: distinguish fitting one solution from learning an operator across problems; neural operators and Transformer-based PDE foundation models, using Poseidon as one example. Reading: our Chapter 04: differentiation; PINN authors: forward and inverse formulations; optional Poseidon: Transformer-based PDE foundation model. |
Recover an unknown physical parameter from a noisy trajectory Start with a forward oscillator, then estimate an unknown parameter from sparse observations. Build data and physics-residual losses with automatic differentiation; enforce initial/boundary conditions, vary loss balance and examine identifiability. Compare a data-only network, a PINN/iPINN and a conventional solver baseline using held-out trajectories and parameter recovery. A small PDE demonstration connects the ODE story to the neural-operator/foundation-model outlook. |
PINN or iPINN competition |
| 14 | Reinforcement learning and preferences Learning through interaction: agents/environments, states, actions, rewards, Markov decision processes, policies, discounted returns and value functions; Bellman equations, exploration/exploitation and tabular Q-learning. Connect temporal-difference learning to neural function approximation and DQN; explain replay buffers and target networks as stabilizing mechanisms. Introduce policy-gradient intuition, reward design and proxy-reward failure. Preference-learning bridge: human comparisons, reward modeling and KL-regularized policy optimization in an RLHF workflow. DPO is an alternative preference objective that avoids explicit reward-model fitting and the RL optimization stage. Detailed DQN training and policy-optimization algorithms are extensions. Reading: Sutton & Barto, Reinforcement Learning: An Introduction (2nd ed.): MDPs, values and temporal-difference learning; Prince: deep reinforcement learning; optional DPO: preferences and an alternative objective. |
Two stories: learn a small game, then learn what a person prefers First calculate temporal-difference targets and implement a tiny Q-learning example; inspect reward design, exploration, evaluation across seeds, and how replay/target networks extend it toward DQN. Then use a small preference dataset to fit a reward score and inspect KL-regularized policy updates against a reference policy. Change preference noise or objective weights and examine reward hacking and behavior. Contrast this workflow with a DPO-style pairwise loss; a toy preference experiment illustrates the mechanism without requiring full language-model training. Report evaluation returns and preference outcomes separately. |
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| 15 | Student-selected frontier investigation Choose one topic in advance: modern computer vision and vision–language models; vision–language–action models; generative models; another advance in ML; or evidence and limitations concerning progress toward more general AI. Optional directions within the student-selected topic include diffusion/generative modeling, graph ML, advanced RL, neural operators, multimodal agents, preference optimization, and production ML/MLOps. Reading: Prince: generative models, diffusion and ethics for a generative-model choice; CLIP for a vision–language choice. A focused primary reading will be selected with students once the topic is chosen. |
Follow one concrete question through a primary paper, a small demonstration or reproducible experiment, and a critique of the evidence. Connect the method to representations, objectives, data and evaluation from earlier weeks. For an AGI-related topic, define the claimed capability and scrutinize its evaluation rather than assume a settled definition or trajectory. | Short final-week lab or tiny project (up to 4 points) Task instructions will be published separately. |
The course has nine laboratory activities, in Weeks 1, 2, 3, 5, 7, 9, 11, 13 and 15. Week 10 has no lab. The CIFAR-10N lab is in Week 7; uncertainty methods return in the Week 12 lecture/tutorial alongside visual prediction. Week 12 has no separate lab. Reinforcement learning also uses tutorial work without an additional lab.
Laboratory workflow
Weeks 1–2 use structured notebook exercises. Agentic coding begins in Week 3 with the first competition-based laboratory. Students remain responsible for validation, verification, interpretation, and reproducibility.
The nine assessed laboratory assignments comprise two introductory labs, six competition-based assignments, and a short final-week lab or tiny project in Week 15. Each is worth up to 4 points, for a maximum of 36 laboratory points. The Week 15 activity is included in this total, not added on top of it.
Rating statement
Policies
Public policy drafts are collected on the Policies page. Final collaboration, AI-agent, competition, accessibility, late-work, and academic-integrity rules require instructor approval.
Footnotes
“Guaranteed (non-burning)” translates the Russian academic term “несгораемая”: the grade is locked in and will not be lowered regardless of final-exam performance.↩︎