Shapelet Attribution

Unlike point-wise attribution methods that highlight isolated time steps, shapelet attribution identifies contiguous subsequences that match a specific, localized pattern. This captures the phase or shape of a signal—such as a specific QRS complex in an ECG or a seasonal dip in sales—rather than just a single anomalous spike. The explanation is a human-interpretable snippet of the original data, making it ideal for domain experts who think in terms of events, not abstract features.

The core mechanism involves discovering shapelets that serve as class-characteristic prototypes. A shapelet is a subsequence that minimizes the distance to one class while maximizing it to others. Attribution is then performed by measuring the distance between a shapelet and the input time series:

• Best-match distance: The minimum Euclidean distance between the shapelet and any sliding window of the same length in the input.
• Decision boundary proximity: The closer the input is to a class-specific shapelet, the stronger the attribution to that class. This provides a case-based reasoning explanation grounded in real data examples.

Shapelet attribution generates a localized saliency map by projecting the shapelet's influence back onto the time axis. The specific segment of the input that best matches the shapelet is highlighted as the primary explanatory region. This is fundamentally different from gradient-based methods:

• Gradient methods produce dense, often noisy importance scores across all time steps.
• Shapelet methods produce sparse, contiguous blocks of high importance, directly mapping to a single interpretable event. This sparsity makes the explanation cognitively easier to process and verify.

Shapelet-based explanations can be derived in two distinct modes:

• Intrinsic interpretability: Using a shapelet-based classifier like a Shapelet Transform or Learning Time-Series Shapelets model, where the learned shapelets are the direct basis for classification and attribution is native.
• Post-hoc model-agnostic: Applying shapelet discovery algorithms to the training data of a black-box model and then using the discovered shapelets as probes to explain the model's decision boundaries via perturbation or distance-based surrogates. This dual nature allows the technique to be applied to both inherently transparent and opaque temporal models.

Modern shapelet attribution relies on efficient discovery algorithms that have evolved beyond brute-force search:

• Gradient-based learning: Methods like Learning Time-Series Shapelets (LTS) treat shapelets as learnable parameters, optimizing their shape directly via stochastic gradient descent to minimize a classification loss.
• Randomized search: Scalable approaches use random projection and pruning to find candidate shapelets in sub-linear time.
• Shapelet transform: A pipeline that extracts the best-matching distances to a set of candidate shapelets as a feature representation, which can then be fed to any classifier with built-in feature importance methods. This optimization focus makes the technique viable for large-scale, high-frequency time-series data.

The final attribution score for a time step is a function of the distance profile between the shapelet and the input. The core metric is: Attribution(t) = f( min_dist(shapelet, X[t:t+L]) ) Where f is typically an exponential decay or a thresholded indicator function. This creates a non-linear importance curve that peaks at the center of the best-matching subsequence and decays rapidly. The sharp localization prevents attribution smearing—a common problem where importance bleeds into adjacent, irrelevant time steps due to temporal correlation.