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+<h2 id="parameters">Parameters</h2> +<dl> +<dt><strong><code>n_states</code></strong> : <code>int</code></dt> +<dd>The number of vertices in the latent space.</dd> +</dl></div> +<details class="source"> +<summary> +<span>Expand source code</span> +</summary> +<pre><code class="python">class Inferer(object): + ''' + The class for doing inference based on posterior estimations. + ''' + + def __init__(self, n_states: int): + ''' + Parameters + ---------- + n_states : int + The number of vertices in the latent space. + ''' + self.n_states = n_states + self.n_categories = int(n_states*(n_states+1)/2) + # self.A, self.B = np.nonzero(np.triu(np.ones(n_states))) + ## indicator of the catagories + self.C = np.triu(np.ones(n_states)) + self.C[self.C>0] = np.arange(self.n_categories) + self.C = self.C.astype(int) + + def build_graphs(self, w_tilde, pc_x, method: str = 'mean', thres: float = 0.5, no_loop: bool = False, + cutoff = 0): + '''Build the backbone. + + Parameters + ---------- + pc_x : np.array + \([N, K]\) The estimated \(p(c_i|Y_i,X_i)\). + method : string, optional + 'mean', 'modified_mean', 'map', or 'modified_map'. + thres : float, optional + The threshold used for filtering edges \(e_{ij}\) that \((n_{i}+n_{j}+e_{ij})/N<thres\), only applied to mean method. + + Retruns + ---------- + G : nx.Graph + The graph of edge scores. + ''' + self.no_loop = no_loop + # self.w_tilde = w_tilde + + graph = np.zeros((self.n_states,self.n_states)) + if method=='mean': + for i in range(self.n_states-1): + for j in range(i+1,self.n_states): + idx = np.sum(pc_x[:,self.C[[i,i,j],[i,j,j]]], axis=1)>=thres + if np.sum(idx)>0: + graph[i,j] = np.mean(pc_x[idx,self.C[i,j]]/np.sum(pc_x[idx][:,self.C[[i,i,j],[i,j,j]]], axis=-1)) + elif method=='modified_mean': + for i in range(self.n_states-1): + for j in range(i+1,self.n_states): + idx = np.sum(pc_x[:,self.C[[i,i,j],[i,j,j]]], axis=1)>=thres + if np.sum(idx)>0: + graph[i,j] = np.sum(pc_x[idx,self.C[i,j]])/np.sum(pc_x[idx][:,self.C[[i,i,j],[i,j,j]]]) + elif method=='map': + c = np.argmax(pc_x, axis=-1) + for i in range(self.n_states-1): + for j in range(i+1,self.n_states): + if np.sum(c==self.C[i,j])>0: + graph[i,j] = np.sum(c==self.C[i,j])/np.sum((c==self.C[i,j])|(c==self.C[i,i])|(c==self.C[j,j])) + elif method=='modified_map': + c = np.argmax(pc_x, axis=-1) + for i in range(self.n_states-1): + for j in range(i+1,self.n_states): + graph[i,j] = np.sum(c==self.C[i,j])/(np.sum((w_tilde[:,i]>0.5)|(w_tilde[:,j]>0.5))+1e-16) + elif method=='raw_map': + c = np.argmax(pc_x, axis=-1) + for i in range(self.n_states-1): + for j in range(i+1,self.n_states): + if np.sum(c==self.C[i,j])>0: + graph[i,j] = np.sum(c==self.C[i,j])/np.sum(np.isin(c, np.diagonal(self.C)) == False) + elif method == "w_base": + for i in range(self.n_states): + for j in range(i+1,self.n_states): + two_vertice_max_w = w_tilde[(np.argmax(w_tilde, axis=1) == i) | (np.argmax(w_tilde, axis=1) == j),:] + num_two_vertice = two_vertice_max_w.shape[0] + if num_two_vertice > 0: + graph[i, j] = np.sum( + np.abs(two_vertice_max_w[:, i] - two_vertice_max_w[:, j]) < 0.1) / num_two_vertice + elif method == "modified_w_base": + top2_idx = np.argpartition(w_tilde, -2, axis=1)[:, -2:] + for i in range(self.n_states): + for j in range(i + 1, self.n_states): + two_vertice_max_w = np.all(top2_idx == [i, j], axis=1) | np.all(top2_idx == [j, i], axis=1) + two_vertice_max_w = w_tilde[two_vertice_max_w, :] + vertice_count = w_tilde[(np.argmax(w_tilde, axis=1) == i) | (np.argmax(w_tilde, axis=1) == j), :] + vertice_count = vertice_count.shape[0] + if vertice_count > 0: + edge_count = \ + np.max((two_vertice_max_w[:, i], two_vertice_max_w[:, j]), axis=0) \ + / (two_vertice_max_w[:, i] + two_vertice_max_w[:, j]) + edge_count = np.sum(edge_count < 0.55) + graph[i, j] = edge_count / vertice_count + else: + raise ValueError("Invalid method, must be one of 'mean', 'modified_mean', 'map', 'modified_map','raw_map','w_base', and 'modified_w_base'.") + + graph[graph<=cutoff] = 0 + G = nx.from_numpy_array(graph) + + if self.no_loop and not nx.is_tree(G): + # prune if there are no loops + G = nx.maximum_spanning_tree(G) + + return G + + def modify_wtilde(self, w_tilde, edges): + '''Project \(\\tilde{w}\) to the estimated backbone. + + Parameters + ---------- + w_tilde : np.array + \([N, k]\) The estimated \(\\tilde{w}\). + edges : np.array + \([|\\mathcal{E}(\\widehat{\\mathcal{B}})|, 2]\). + + Retruns + ---------- + w : np.array + The projected \(\\tilde{w}\). + ''' + w = np.zeros_like(w_tilde) + + # projection on nodes + best_proj_err_node = np.sum(w_tilde**2, axis=-1) - 2*np.max(w_tilde, axis=-1) +1 + best_proj_err_node_ind = np.argmax(w_tilde, axis=-1) + + if len(edges)>0: + # projection on edges + idc = np.tile(np.arange(w.shape[0]), (2,1)).T + ide = edges[np.argmax(np.sum(w_tilde[:,edges], axis=-1)**2 - + 4 * np.prod(w_tilde[:,edges], axis=-1) + + 2 * np.sum(w_tilde[:,edges], axis=-1), axis=-1)] + w[idc, ide] = w_tilde[idc, ide] + (1-np.sum(w_tilde[idc, ide], axis=-1, keepdims=True))/2 + best_proj_err_edge = np.sum(w_tilde**2, axis=-1) - np.sum(w_tilde[idc, ide]**2, axis=-1) + (1-np.sum(w_tilde[idc, ide], axis=-1))**2/2 + + idc = (best_proj_err_node<best_proj_err_edge) + w[idc,:] = np.eye(w_tilde.shape[-1])[best_proj_err_node_ind[idc]] + else: + idc = np.arange(w.shape[0]) + w[idc, best_proj_err_node_ind] = 1 + return w + + + def build_milestone_net(self, subgraph, init_node: int): + '''Build the milestone network. + + Parameters + ---------- + subgraph : nx.Graph + The connected component of the backbone given the root vertex. + init_node : int + The root vertex. + + Returns + ---------- + df_subgraph : pd.DataFrame + The milestone network. + ''' + if len(subgraph)==1: + warnings.warn('Singular node.') + return [] + elif nx.is_directed_acyclic_graph(subgraph): + milestone_net = [] + for edge in list(subgraph.edges): + if edge[0]==init_node: + dist = 1 + elif edge[1]==init_node: + paths_0 = nx.all_simple_paths(subgraph, source=init_node, target=edge[0]) + dist = - (np.max([len(p) for p in paths_1]) - 1) + else: + paths_0 = nx.all_simple_paths(subgraph, source=init_node, target=edge[0]) + paths_1 = nx.all_simple_paths(subgraph, source=init_node, target=edge[1]) + dist = np.max([len(p) for p in paths_1]) - np.max([len(p) for p in paths_0]) + milestone_net.append([edge[0], edge[1], dist]) + else: + # Dijkstra's Algorithm to find the shortest path + unvisited = {node: {'parent':None, + 'score':np.inf, + 'distance':np.inf} for node in subgraph.nodes} + current = init_node + currentScore = 0 + currentDistance = 0 + unvisited[current]['score'] = currentScore + + milestone_net = [] + while True: + for neighbour in subgraph.neighbors(current): + if neighbour not in unvisited: continue + newScore = currentScore + subgraph[current][neighbour]['weight'] + if unvisited[neighbour]['score'] > newScore: + unvisited[neighbour]['score'] = newScore + unvisited[neighbour]['parent'] = current + unvisited[neighbour]['distance'] = currentDistance+1 + + if len(unvisited)<len(subgraph): + milestone_net.append([unvisited[current]['parent'], + current, + unvisited[current]['distance']]) + del unvisited[current] + if not unvisited: break + current, currentScore, currentDistance = \ + sorted([(i[0],i[1]['score'],i[1]['distance']) for i in unvisited.items()], + key = lambda x: x[1])[0] + return np.array(milestone_net) + + + def comp_pseudotime(self, milestone_net, init_node: int, w): + '''Compute pseudotime. + + Parameters + ---------- + milestone_net : pd.DataFrame + The milestone network. + init_node : int + The root vertex. + w : np.array + \([N, k]\) The projected \(\\tilde{w}\). + + Returns + ---------- + pseudotime : np.array + \([N, k]\) The estimated pseudtotime. + ''' + pseudotime = np.empty(w.shape[0]) + pseudotime.fill(np.nan) + pseudotime[w[:,init_node]==1] = 0 + + if len(milestone_net)>0: + for i in range(len(milestone_net)): + _from, _to = milestone_net[i,:2] + _from, _to = int(_from), int(_to) + + idc = ((w[:,_from]>0)&(w[:,_to]>0)) | (w[:,_to]==1) + pseudotime[idc] = w[idc,_to] + milestone_net[i,-1] - 1 + + return pseudotime</code></pre> +</details> +<h3>Methods</h3> +<dl> +<dt id="VITAE.inference.Inferer.build_graphs"><code class="name flex"> +<span>def <span class="ident">build_graphs</span></span>(<span>self, w_tilde, pc_x, method: str = 'mean', thres: float = 0.5, no_loop: bool = False, cutoff=0)</span> +</code></dt> +<dd> +<div class="desc"><p>Build the backbone.</p> +<h2 id="parameters">Parameters</h2> +<dl> +<dt><strong><code>pc_x</code></strong> : <code>np.array</code></dt> +<dd><span><span class="MathJax_Preview">[N, K]</span><script type="math/tex">[N, K]</script></span> The estimated <span><span class="MathJax_Preview">p(c_i|Y_i,X_i)</span><script type="math/tex">p(c_i|Y_i,X_i)</script></span>.</dd> +<dt><strong><code>method</code></strong> : <code>string</code>, optional</dt> +<dd>'mean', 'modified_mean', 'map', or 'modified_map'.</dd> +<dt><strong><code>thres</code></strong> : <code>float</code>, optional</dt> +<dd>The threshold used for filtering edges <span><span class="MathJax_Preview">e_{ij}</span><script type="math/tex">e_{ij}</script></span> that <span><span class="MathJax_Preview">(n_{i}+n_{j}+e_{ij})/N<thres</span><script type="math/tex">(n_{i}+n_{j}+e_{ij})/N<thres</script></span>, only applied to mean method.</dd> +</dl> +<h2 id="retruns">Retruns</h2> +<p>G : nx.Graph +The graph of edge scores.</p></div> +</dd> +<dt id="VITAE.inference.Inferer.modify_wtilde"><code class="name flex"> +<span>def <span class="ident">modify_wtilde</span></span>(<span>self, w_tilde, edges)</span> +</code></dt> +<dd> +<div class="desc"><p>Project <span><span class="MathJax_Preview">\tilde{w}</span><script type="math/tex">\tilde{w}</script></span> to the estimated backbone.</p> +<h2 id="parameters">Parameters</h2> +<dl> +<dt><strong><code>w_tilde</code></strong> : <code>np.array</code></dt> +<dd><span><span class="MathJax_Preview">[N, k]</span><script type="math/tex">[N, k]</script></span> The estimated <span><span class="MathJax_Preview">\tilde{w}</span><script type="math/tex">\tilde{w}</script></span>.</dd> +<dt><strong><code>edges</code></strong> : <code>np.array</code></dt> +<dd><span><span class="MathJax_Preview">[|\mathcal{E}(\widehat{\mathcal{B}})|, 2]</span><script type="math/tex">[|\mathcal{E}(\widehat{\mathcal{B}})|, 2]</script></span>.</dd> +</dl> +<h2 id="retruns">Retruns</h2> +<p>w : np.array +The projected <span><span class="MathJax_Preview">\tilde{w}</span><script type="math/tex">\tilde{w}</script></span>.</p></div> +</dd> +<dt id="VITAE.inference.Inferer.build_milestone_net"><code class="name flex"> +<span>def <span class="ident">build_milestone_net</span></span>(<span>self, subgraph, init_node: int)</span> +</code></dt> +<dd> +<div class="desc"><p>Build the milestone network.</p> +<h2 id="parameters">Parameters</h2> +<dl> +<dt><strong><code>subgraph</code></strong> : <code>nx.Graph</code></dt> +<dd>The connected component of the backbone given the root vertex.</dd> +<dt><strong><code>init_node</code></strong> : <code>int</code></dt> +<dd>The root vertex.</dd> +</dl> +<h2 id="returns">Returns</h2> +<dl> +<dt><strong><code>df_subgraph</code></strong> : <code>pd.DataFrame </code></dt> +<dd>The milestone network.</dd> +</dl></div> +</dd> +<dt id="VITAE.inference.Inferer.comp_pseudotime"><code class="name flex"> +<span>def <span class="ident">comp_pseudotime</span></span>(<span>self, milestone_net, init_node: int, w)</span> +</code></dt> +<dd> +<div class="desc"><p>Compute pseudotime.</p> +<h2 id="parameters">Parameters</h2> +<dl> +<dt><strong><code>milestone_net</code></strong> : <code>pd.DataFrame</code></dt> +<dd>The milestone network.</dd> +<dt><strong><code>init_node</code></strong> : <code>int</code></dt> +<dd>The root vertex.</dd> +<dt><strong><code>w</code></strong> : <code>np.array</code></dt> +<dd><span><span class="MathJax_Preview">[N, k]</span><script type="math/tex">[N, k]</script></span> The projected <span><span class="MathJax_Preview">\tilde{w}</span><script type="math/tex">\tilde{w}</script></span>.</dd> +</dl> +<h2 id="returns">Returns</h2> +<dl> +<dt><strong><code>pseudotime</code></strong> : <code>np.array</code></dt> +<dd><span><span class="MathJax_Preview">[N, k]</span><script type="math/tex">[N, k]</script></span> The estimated pseudtotime.</dd> +</dl></div> +</dd> +</dl> +</dd> +</dl> +</section> +</article> +<nav id="sidebar"> +<div class="toc"> +<ul></ul> +</div> +<ul id="index"> +<li><h3>Super-module</h3> +<ul> +<li><code><a title="VITAE" href="index.html">VITAE</a></code></li> +</ul> +</li> +<li><h3><a href="#header-classes">Classes</a></h3> +<ul> +<li> +<h4><code><a title="VITAE.inference.Inferer" href="#VITAE.inference.Inferer">Inferer</a></code></h4> +<ul class=""> +<li><code><a title="VITAE.inference.Inferer.build_graphs" href="#VITAE.inference.Inferer.build_graphs">build_graphs</a></code></li> +<li><code><a title="VITAE.inference.Inferer.modify_wtilde" href="#VITAE.inference.Inferer.modify_wtilde">modify_wtilde</a></code></li> +<li><code><a title="VITAE.inference.Inferer.build_milestone_net" href="#VITAE.inference.Inferer.build_milestone_net">build_milestone_net</a></code></li> +<li><code><a title="VITAE.inference.Inferer.comp_pseudotime" href="#VITAE.inference.Inferer.comp_pseudotime">comp_pseudotime</a></code></li> +</ul> +</li> +</ul> +</li> +</ul> +</nav> +</main> +<footer id="footer"> +<p>Generated by <a href="https://pdoc3.github.io/pdoc" title="pdoc: Python API documentation generator"><cite>pdoc</cite> 0.11.1</a>.</p> +</footer> +</body> +</html>