Algorithm 1.

Our unsupervised seizure identification algorithm. We employ a variational autoencoder architecture comprising an encoder network $g_{\mathit{\varphi }}:{ℝ}^{M\times T}\to {ℝ}^{2\times D}$ and a decoder network $p_{\mathit{\theta }}:{ℝ}^D\to {ℝ}^{M\times T}$, with trainable parameters $\mathit{\varphi }\in {ℝ}^{d_g}$ and $\mathit{\theta }\in {ℝ}^{d_p}$, respectively. We train our architecture on EEG recordings that do not contain any seizures, employing a sparsity-enforcing loss function to suppress EEG artifacts (c.f. Section (3)). As training captures non-seizure activity, we identify seizures w.r.t. the reconstruction errors at inference time.

1:	procedure Training (${\mathit{X}}^{(i)}\in {ℝ}^{M\times T}$ for $i\in$ non-seizure training recordings, $g_{\mathit{\varphi }}$, $p_{\mathit{\theta }}$)
2:	Initialize trainable parameters $\mathit{\varphi }$ and $\mathit{\theta }$
3:	repeat
4:	Sample recording ${\mathit{X}}^{(i)}$ from non-seizure training recordings
5:	Sample auxiliary variables ${ϵ}^{(l)}\sim \mathcal{N}(\mathbf{0},\mathit{I})$, $l\in \{1,\dots ,L\}$
6:	Reparametrize to obtain latent features ${\mathit{z}}^{(l)}=\mathit{\mu }+\mathit{\sigma }\otimes {ϵ}^{(l)}$, $l\in \{1,\dots ,L\}$
7:	Compute sparsity-enforcing loss (2) and its gradients w.r.t. $\sim \mathit{\varphi }$ and $\mathit{\theta }$
8:	Update trainable parameters $\mathit{\varphi }$ and $\mathit{\theta }$ via Adam optimization
9:	until Loss value (2) converged
10:	return Trained $g_{\mathit{\varphi }}$, Trained $p_{\mathit{\theta }}$
11:	end procedure
1:	procedure Inference (${\mathit{X}}^{(i)}\in {ℝ}^{M\times T}$ for $i\in$ test recordings, Trained $g_{\mathit{\varphi }}$, Trained $p_{\mathit{\theta }}$)
2:	repeat
3:	Sample recording ${\mathit{X}}^{(i)}$ from test recordings
4:	Sample auxiliary variables ${ϵ}^{(l)}\sim \mathcal{N}(\mathbf{0},\mathit{I})$, $l\in \{1,\dots ,L\}$
5:	Reparametrize to obtain latent features ${\mathit{z}}^{(l)}=\mathit{\mu }+\mathit{\sigma }\otimes {ϵ}^{(l)}$, $l\in \{1,\dots ,L\}$
6:	Compute ${\widehat{\mathit{X}}}^{(i,l)}$ for each ${\mathit{z}}^{(l)}$
7:	Compute decoder reconstruction ${\widehat{\mathit{X}}}^{(i)}$ by averaging ${\widehat{\mathit{X}}}^{(i,l)}$ over $l\in \{1,\dots ,L\}$
8:	Compute seizure evidence score (3) w.r.t.~the reconstruction error between ${\mathit{X}}^{(i)}$ and ${\widehat{\mathit{X}}}^{(i)}$
9:	until All recordings are tested
10:	return Seizure evidence scores for all test recordings
11:	end procedure