Event detection in biosignals

"A heartbeat detected 40 milliseconds late is still a heartbeat. A seizure declared a second early is a lie the clock will expose."

A Punctual AI Agent

You should be comfortable with sampling, timestamps, and jitter from Chapter 3, and with the vocabulary of change points and residual thresholds from Chapter 12. Event detection is a specialization of that machinery under a hard constraint: the ground truth is a set of time-stamped labels, not a per-sample mask, and the timing tolerance is set by physiology.

What counts as an event, and what shape it has

Events come in two geometries, and confusing them is the most common modeling error in this space. A point event has a single canonical instant: the R-peak of a QRS complex, the systolic foot of a PPG pulse, a footstep-driven motion spike. An interval event has an onset and an offset that both matter: an apnea lasting eleven seconds, an epileptic seizure lasting ninety, an atrial-fibrillation episode lasting minutes. Point events are scored on localization error; interval events are scored on overlap. If you treat a seizure as a point ("it happened somewhere in this minute") you throw away the onset timing a neurologist needs; if you treat every apnea as an interval to be perfectly bounded you will be punished for a half-second of offset ambiguity that no scorer actually cares about.

The physiological time constant sets the tolerance. R-peaks must be localized to roughly \(\pm 50\) ms because the inter-beat interval itself carries the signal, and a 50 ms error is already a few percent of a typical 800 ms beat. Apnea offsets, by contrast, are comfortable with a tolerance of a second or more. Always ask "what does the downstream metric integrate over?" before choosing a representation.

Detection paradigms: from transforms to learned models

The classical workhorse for point events is the transform-and-threshold pipeline, and the canonical example is the Pan-Tompkins QRS detector. It bandpass filters to isolate QRS energy (roughly 5 to 15 Hz), differentiates to emphasize the steep slope of the R-wave, squares to make everything positive and to amplify large slopes, integrates over a moving window to capture waveform width, and then applies an adaptive threshold with physiological refractory logic (no two beats within 200 ms). Its enduring value is that it is interpretable, runs in a handful of arithmetic operations per sample, and degrades gracefully. The relatives of this idea live throughout: matched filters and template correlation for stereotyped morphologies, and the CUSUM and residual-threshold detectors from Chapter 12 for onset detection when the event is defined by a change in signal statistics.

Learned detectors take over when morphology is variable or context matters. Sequence models that emit a per-sample probability, then post-process peaks, are the modern default: temporal convolutional networks and recurrent models from Chapter 14 map a raw or lightly filtered window to a dense "eventness" curve. The key subtlety is that the network output is not the answer; it is an intermediate density that still needs peak-picking or interval-thresholding with the same refractory and tolerance logic the classical detector used. The deep model buys robustness to morphology and noise; it does not free you from the timing post-processor.

Scoring: matching, tolerance, and the imbalance trap

To score point events, you match each reference instant to at most one prediction within a tolerance \(\tau\). A matched pair is a true positive; an unmatched reference is a false negative (a miss); an unmatched prediction is a false positive. From these you compute sensitivity and positive predictive value, and their harmonic mean, the event-level \(F_1\):

Two rules keep this honest. First, matching must be one-to-one; a greedy nearest-neighbor assignment (or, for the strict case, a Hungarian assignment) prevents one lucky prediction from claiming credit for several nearby references. Second, tolerance must be justified by physiology, stated explicitly, and held constant across systems you compare. For interval events, replace the point tolerance with an overlap criterion, typically that predicted and reference intervals share at least some minimum fraction of their union, echoing the intersection-over-union idea used elsewhere in the book.

Because events are rare, per-sample metrics lie by omission. Accuracy and even per-sample AUC are dominated by the vast "nothing happening" background and can look excellent while the detector misses most events. Report event-level sensitivity and false events per hour (or per night), never bare accuracy. And remember from Chapter 5 that windows from the same patient must not straddle the train and test split; the very next section, on patient-level splits, makes this failure mode concrete.

import numpy as np

def match_events(ref, pred, tol):
    """One-to-one greedy matching of point events within tolerance `tol`.
    ref, pred: sorted 1-D arrays of event times (same units as tol)."""
    ref, pred = np.sort(ref), np.sort(pred)
    used = np.zeros(len(pred), dtype=bool)
    tp = 0
    for t in ref:
        # nearest unused prediction
        cand = np.where(~used)[0]
        if cand.size == 0:
            break
        j = cand[np.argmin(np.abs(pred[cand] - t))]
        if abs(pred[j] - t) <= tol:
            used[j] = True
            tp += 1
    fn = len(ref) - tp
    fp = len(pred) - tp
    f1 = 2 * tp / (2 * tp + fp + fn) if (2 * tp + fp + fn) else 0.0
    return dict(tp=tp, fp=fp, fn=fn, f1=round(f1, 3))

ref  = np.array([1.00, 2.00, 3.00, 4.00])   # reference R-peaks (s)
pred = np.array([1.03, 2.05, 3.60, 4.02])   # detector output (s)
print(match_events(ref, pred, tol=0.050))   # 3.60 is a miss + a false event

Streaming, latency, and the causal constraint

An offline detector may look at the whole recording; a wearable or a bedside monitor cannot. Online detection is causal: at time \(t\) you may use only samples up to \(t\), and you often must declare the event within a bounded latency to be useful (a fall alarm two minutes late is worthless). This forces three compromises. You lose the smoothing benefit of future context, so causal detectors are noisier at onset. You must fix a decision latency budget and accept that longer budgets buy accuracy. And you must handle the artifacts from the previous sections online, because a motion spike that a human would ignore will trigger a false alarm at 3 a.m. Streaming inference and the online-update machinery in Chapter 60 are the natural home for these detectors once they leave the research notebook.

What's Next

In Section 28.5, we turn to where the reference events themselves come from: clinical labels and reference standards. Every tolerance and every matched-pair count in this section quietly assumed a trustworthy ground truth, and the next section confronts how that truth is made, how much annotators disagree, and what a "gold standard" is actually worth.