Kernel embeddings for learning machines achieve strong performance through their representational power. To leverage this, Lopez-Paz et al. introduced kernel-based embeddings for feature construction in pairwise causal discovery. Starting from a dataset of empirical joint distributions S = { (x_{ij},y_{ij}){j=1}^{n_i} }{i=1}^n, a kernel mean embedding projects all these distributions into the same Reproducing Kernel Hilbert Space (RKHS) $\mathcal{H}_k$. To obtain a homogeneous, low-dimensional embedding, random cosine-based embeddings are used to approximate empirical kernel mean embeddings: $\mu_{k,m}(P_{S_j}) = \frac{2C_k}{|S|} \sum_{x_{ij},y_{ij} \in S_j} (\cos (w_j^x \ast x_{ij} + w_j^y \ast y_{ij} + b_j))_{j=1}^m \in \mathbb{R}^m$ where $\mu_{k,m}(P_{S_j})$ is the kernel mean embedding of the empirical distribution $P_{S_j}$, and $m$ defines the number of dimensions of the output space. The kernel parameters $\left\{w_j, b_j\right\}_{j=1}^m$ are sampled i.i.d. from $\mathbb{N}_{0,2} \times [0, 2\pi]$. Finally, $C_k = \int_{\mathcal{L}} p_k(w)dw$ with p_k : mathbb{R}^d rightarrow mathbb{R} being the positive and integrable Fourier transform of the chosen kernel $k$ (equal to 1 in this case).