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<article id="content">





  
  

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<header>





  
  

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<h1 class="title">Module <code>VITAE.inference</code></h1>





  
  

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</header>





  
  

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<section id="section-intro">





  
  

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</section>





  
  

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<section>





  
  

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</section>





  
  

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<section>





  
  

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</section>





  
  

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<section>





  
  

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</section>





  
  

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<section>





  
  

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<h2 class="section-title" id="header-classes">Classes</h2>





  
  

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<dl>





  
  

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<dt id="VITAE.inference.Inferer"><code class="flex name class">





  
  

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<span>class <span class="ident">Inferer</span></span>





  
  

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<span>(</span><span>n_states: int)</span>





  
  

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</code></dt>





  
  

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<dd>





  
  

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<div class="desc"><p>The class for doing inference based on posterior estimations.</p>





  
  

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<h2 id="parameters">Parameters</h2>





  
  

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<dl>





  
  

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<dt><strong><code>n_states</code></strong> :&ensp;<code>int</code></dt>





  
  

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<dd>The number of vertices in the latent space.</dd>





  
  

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</dl></div>





  
  

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<details class="source">





  
  

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<summary>





  
  

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<span>Expand source code</span>





  
  

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</summary>





  
  

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<pre><code class="python">class Inferer(object):





  
  

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    &#39;&#39;&#39;





  
  

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    The class for doing inference based on posterior estimations.





  
  

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    &#39;&#39;&#39;





  
  

  59
  





  
  

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    def __init__(self, n_states: int):





  
  

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        &#39;&#39;&#39;





  
  

  62
  
        Parameters





  
  

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        ----------





  
  

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        n_states : int





  
  

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            The number of vertices in the latent space.





  
  

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        &#39;&#39;&#39;        





  
  

  67
  
        self.n_states = n_states





  
  

  68
  
        self.n_categories = int(n_states*(n_states+1)/2)





  
  

  69
  
      #  self.A, self.B = np.nonzero(np.triu(np.ones(n_states)))





  
  

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       ## indicator of the catagories





  
  

  71
  
        self.C = np.triu(np.ones(n_states))





  
  

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        self.C[self.C&gt;0] = np.arange(self.n_categories)





  
  

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        self.C = self.C.astype(int)





  
  

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    def build_graphs(self, w_tilde, pc_x, method: str = &#39;mean&#39;, thres: float = 0.5, no_loop: bool = False, 





  
  

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            cutoff = 0):





  
  

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        &#39;&#39;&#39;Build the backbone.





  
  

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        Parameters





  
  

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        ----------





  
  

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        pc_x : np.array





  
  

  82
  
            \([N, K]\) The estimated \(p(c_i|Y_i,X_i)\).        





  
  

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        method : string, optional 





  
  

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            &#39;mean&#39;, &#39;modified_mean&#39;, &#39;map&#39;, or &#39;modified_map&#39;.





  
  

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        thres : float, optional 





  
  

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            The threshold used for filtering edges \(e_{ij}\) that \((n_{i}+n_{j}+e_{ij})/N&lt;thres\), only applied to mean method.





  
  

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        Retruns





  
  

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        ----------





  
  

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        G : nx.Graph





  
  

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            The graph of edge scores.





  
  

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        &#39;&#39;&#39;





  
  

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        self.no_loop = no_loop





  
  

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    #    self.w_tilde = w_tilde





  
  

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        graph = np.zeros((self.n_states,self.n_states))





  
  

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        if method==&#39;mean&#39;:





  
  

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            for i in range(self.n_states-1):





  
  

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                for j in range(i+1,self.n_states):





  
  

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                    idx = np.sum(pc_x[:,self.C[[i,i,j],[i,j,j]]], axis=1)&gt;=thres





  
  

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                    if np.sum(idx)&gt;0:





  
  

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                        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))





  
  

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        elif method==&#39;modified_mean&#39;:





  
  

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            for i in range(self.n_states-1):





  
  

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                for j in range(i+1,self.n_states):





  
  

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                    idx = np.sum(pc_x[:,self.C[[i,i,j],[i,j,j]]], axis=1)&gt;=thres





  
  

  107
  
                    if np.sum(idx)&gt;0:





  
  

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                        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]]])





  
  

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        elif method==&#39;map&#39;:





  
  

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            c = np.argmax(pc_x, axis=-1)





  
  

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            for i in range(self.n_states-1):





  
  

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                for j in range(i+1,self.n_states):





  
  

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                    if np.sum(c==self.C[i,j])&gt;0:





  
  

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                        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]))





  
  

  115
  
        elif method==&#39;modified_map&#39;:





  
  

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            c = np.argmax(pc_x, axis=-1)





  
  

  117
  
            for i in range(self.n_states-1):





  
  

  118
  
                for j in range(i+1,self.n_states):





  
  

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                    graph[i,j] = np.sum(c==self.C[i,j])/(np.sum((w_tilde[:,i]&gt;0.5)|(w_tilde[:,j]&gt;0.5))+1e-16)





  
  

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        elif method==&#39;raw_map&#39;:





  
  

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            c = np.argmax(pc_x, axis=-1)





  
  

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            for i in range(self.n_states-1):





  
  

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                for j in range(i+1,self.n_states):





  
  

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                    if np.sum(c==self.C[i,j])&gt;0:





  
  

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                        graph[i,j] = np.sum(c==self.C[i,j])/np.sum(np.isin(c, np.diagonal(self.C)) == False)





  
  

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        elif method == &#34;w_base&#34;:





  
  

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            for i in range(self.n_states):





  
  

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                for j in range(i+1,self.n_states):





  
  

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                    two_vertice_max_w = w_tilde[(np.argmax(w_tilde, axis=1) == i) | (np.argmax(w_tilde, axis=1) == j),:]





  
  

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                    num_two_vertice = two_vertice_max_w.shape[0]





  
  

  131
  
                    if num_two_vertice &gt; 0:





  
  

  132
  
                        graph[i, j] = np.sum(





  
  

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                            np.abs(two_vertice_max_w[:, i] - two_vertice_max_w[:, j]) &lt; 0.1) / num_two_vertice





  
  

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        elif method == &#34;modified_w_base&#34;:





  
  

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            top2_idx = np.argpartition(w_tilde, -2, axis=1)[:, -2:]





  
  

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            for i in range(self.n_states):





  
  

  137
  
                for j in range(i + 1, self.n_states):





  
  

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                    two_vertice_max_w = np.all(top2_idx == [i, j], axis=1) | np.all(top2_idx == [j, i], axis=1)





  
  

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                    two_vertice_max_w = w_tilde[two_vertice_max_w, :]





  
  

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                    vertice_count = w_tilde[(np.argmax(w_tilde, axis=1) == i) | (np.argmax(w_tilde, axis=1) == j), :]





  
  

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                    vertice_count = vertice_count.shape[0]





  
  

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                    if vertice_count &gt; 0:





  
  

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                        edge_count = \





  
  

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                            np.max((two_vertice_max_w[:, i], two_vertice_max_w[:, j]), axis=0) \





  
  

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                            / (two_vertice_max_w[:, i] + two_vertice_max_w[:, j])





  
  

  146
  
                        edge_count = np.sum(edge_count &lt; 0.55)





  
  

  147
  
                        graph[i, j] = edge_count / vertice_count





  
  

  148
  
        else:





  
  

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            raise ValueError(&#34;Invalid method, must be one of &#39;mean&#39;, &#39;modified_mean&#39;, &#39;map&#39;, &#39;modified_map&#39;,&#39;raw_map&#39;,&#39;w_base&#39;, and &#39;modified_w_base&#39;.&#34;)





  
  

  150
  
        





  
  

  151
  
        graph[graph&lt;=cutoff] = 0





  
  

  152
  
        G = nx.from_numpy_array(graph)





  
  

  153
  
        





  
  

  154
  
        if self.no_loop and not nx.is_tree(G):





  
  

  155
  
            # prune if there are no loops





  
  

  156
  
            G = nx.maximum_spanning_tree(G)





  
  

  157
  
            





  
  

  158
  
        return G





  
  

  159
  





  
  

  160
  
    def modify_wtilde(self, w_tilde, edges):





  
  

  161
  
        &#39;&#39;&#39;Project \(\\tilde{w}\) to the estimated backbone.





  
  

  162
  
        





  
  

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        Parameters





  
  

  164
  
        ----------





  
  

  165
  
        w_tilde : np.array





  
  

  166
  
            \([N, k]\) The estimated \(\\tilde{w}\).        





  
  

  167
  
        edges : np.array





  
  

  168
  
            \([|\\mathcal{E}(\\widehat{\\mathcal{B}})|, 2]\).





  
  

  169
  





  
  

  170
  
        Retruns





  
  

  171
  
        ----------





  
  

  172
  
        w : np.array





  
  

  173
  
            The projected \(\\tilde{w}\).





  
  

  174
  
        &#39;&#39;&#39;





  
  

  175
  
        w = np.zeros_like(w_tilde)





  
  

  176
  
        





  
  

  177
  
        # projection on nodes





  
  

  178
  
        best_proj_err_node = np.sum(w_tilde**2, axis=-1) - 2*np.max(w_tilde, axis=-1) +1





  
  

  179
  
        best_proj_err_node_ind = np.argmax(w_tilde, axis=-1)





  
  

  180
  
        





  
  

  181
  
        if len(edges)&gt;0:





  
  

  182
  
            # projection on edges





  
  

  183
  
            idc = np.tile(np.arange(w.shape[0]), (2,1)).T





  
  

  184
  
            ide = edges[np.argmax(np.sum(w_tilde[:,edges], axis=-1)**2 -





  
  

  185
  
                                  4 * np.prod(w_tilde[:,edges], axis=-1) +





  
  

  186
  
                                  2 * np.sum(w_tilde[:,edges], axis=-1), axis=-1)]





  
  

  187
  
            w[idc, ide] = w_tilde[idc, ide] + (1-np.sum(w_tilde[idc, ide], axis=-1, keepdims=True))/2





  
  

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            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





  
  

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  190
  
            idc = (best_proj_err_node&lt;best_proj_err_edge)





  
  

  191
  
            w[idc,:] = np.eye(w_tilde.shape[-1])[best_proj_err_node_ind[idc]]





  
  

  192
  
        else:





  
  

  193
  
            idc = np.arange(w.shape[0])





  
  

  194
  
            w[idc, best_proj_err_node_ind] = 1





  
  

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        return w





  
  

  196
  





  
  

  197
  
     





  
  

  198
  
    def build_milestone_net(self, subgraph, init_node: int):





  
  

  199
  
        &#39;&#39;&#39;Build the milestone network.





  
  

  200
  





  
  

  201
  
        Parameters





  
  

  202
  
        ----------





  
  

  203
  
        subgraph : nx.Graph





  
  

  204
  
            The connected component of the backbone given the root vertex.





  
  

  205
  
        init_node : int





  
  

  206
  
            The root vertex.





  
  

  207
  
        





  
  

  208
  
        Returns





  
  

  209
  
        ----------





  
  

  210
  
        df_subgraph : pd.DataFrame 





  
  

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            The milestone network.





  
  

  212
  
        &#39;&#39;&#39;





  
  

  213
  
        if len(subgraph)==1:





  
  

  214
  
            warnings.warn(&#39;Singular node.&#39;)





  
  

  215
  
            return []





  
  

  216
  
        elif nx.is_directed_acyclic_graph(subgraph):





  
  

  217
  
            milestone_net = []





  
  

  218
  
            for edge in list(subgraph.edges):





  
  

  219
  
                if edge[0]==init_node:





  
  

  220
  
                    dist = 1





  
  

  221
  
                elif edge[1]==init_node:





  
  

  222
  
                    paths_0 = nx.all_simple_paths(subgraph, source=init_node, target=edge[0])





  
  

  223
  
                    dist = - (np.max([len(p) for p in paths_1]) - 1)





  
  

  224
  
                else:





  
  

  225
  
                    paths_0 = nx.all_simple_paths(subgraph, source=init_node, target=edge[0])





  
  

  226
  
                    paths_1 = nx.all_simple_paths(subgraph, source=init_node, target=edge[1])





  
  

  227
  
                    dist = np.max([len(p) for p in paths_1]) - np.max([len(p) for p in paths_0])





  
  

  228
  
                milestone_net.append([edge[0], edge[1], dist])





  
  

  229
  
        else:





  
  

  230
  
            # Dijkstra&#39;s Algorithm to find the shortest path





  
  

  231
  
            unvisited = {node: {&#39;parent&#39;:None,





  
  

  232
  
                                &#39;score&#39;:np.inf,





  
  

  233
  
                                &#39;distance&#39;:np.inf} for node in subgraph.nodes}





  
  

  234
  
            current = init_node





  
  

  235
  
            currentScore = 0





  
  

  236
  
            currentDistance = 0





  
  

  237
  
            unvisited[current][&#39;score&#39;] = currentScore





  
  

  238
  





  
  

  239
  
            milestone_net = []





  
  

  240
  
            while True:





  
  

  241
  
                for neighbour in subgraph.neighbors(current):





  
  

  242
  
                    if neighbour not in unvisited: continue





  
  

  243
  
                    newScore = currentScore + subgraph[current][neighbour][&#39;weight&#39;]





  
  

  244
  
                    if unvisited[neighbour][&#39;score&#39;] &gt; newScore:





  
  

  245
  
                        unvisited[neighbour][&#39;score&#39;] = newScore





  
  

  246
  
                        unvisited[neighbour][&#39;parent&#39;] = current





  
  

  247
  
                        unvisited[neighbour][&#39;distance&#39;] = currentDistance+1





  
  

  248
  





  
  

  249
  
                if len(unvisited)&lt;len(subgraph):





  
  

  250
  
                    milestone_net.append([unvisited[current][&#39;parent&#39;],





  
  

  251
  
                                          current,





  
  

  252
  
                                          unvisited[current][&#39;distance&#39;]])





  
  

  253
  
                del unvisited[current]





  
  

  254
  
                if not unvisited: break





  
  

  255
  
                current, currentScore, currentDistance = \





  
  

  256
  
                    sorted([(i[0],i[1][&#39;score&#39;],i[1][&#39;distance&#39;]) for i in unvisited.items()],





  
  

  257
  
                            key = lambda x: x[1])[0]





  
  

  258
  
            return np.array(milestone_net)





  
  

  259
  
    





  
  

  260
  





  
  

  261
  
    def comp_pseudotime(self, milestone_net, init_node: int, w):





  
  

  262
  
        &#39;&#39;&#39;Compute pseudotime.





  
  

  263
  





  
  

  264
  
        Parameters





  
  

  265
  
        ----------





  
  

  266
  
        milestone_net : pd.DataFrame





  
  

  267
  
            The milestone network.





  
  

  268
  
        init_node : int





  
  

  269
  
            The root vertex.





  
  

  270
  
        w : np.array





  
  

  271
  
            \([N, k]\) The projected \(\\tilde{w}\).





  
  

  272
  
        





  
  

  273
  
        Returns





  
  

  274
  
        ----------





  
  

  275
  
        pseudotime : np.array





  
  

  276
  
            \([N, k]\) The estimated pseudtotime.





  
  

  277
  
        &#39;&#39;&#39;





  
  

  278
  
        pseudotime = np.empty(w.shape[0])





  
  

  279
  
        pseudotime.fill(np.nan)





  
  

  280
  
        pseudotime[w[:,init_node]==1] = 0





  
  

  281
  
        





  
  

  282
  
        if len(milestone_net)&gt;0:





  
  

  283
  
            for i in range(len(milestone_net)):





  
  

  284
  
                _from, _to = milestone_net[i,:2]





  
  

  285
  
                _from, _to = int(_from), int(_to)





  
  

  286
  





  
  

  287
  
                idc = ((w[:,_from]&gt;0)&amp;(w[:,_to]&gt;0)) | (w[:,_to]==1)





  
  

  288
  
                pseudotime[idc] = w[idc,_to] + milestone_net[i,-1] - 1





  
  

  289
  
        





  
  

  290
  
        return pseudotime</code></pre>





  
  

  291
  
</details>





  
  

  292
  
<h3>Methods</h3>





  
  

  293
  
<dl>





  
  

  294
  
<dt id="VITAE.inference.Inferer.build_graphs"><code class="name flex">





  
  

  295
  
<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>





  
  

  296
  
</code></dt>





  
  

  297
  
<dd>





  
  

  298
  
<div class="desc"><p>Build the backbone.</p>





  
  

  299
  
<h2 id="parameters">Parameters</h2>





  
  

  300
  
<dl>





  
  

  301
  
<dt><strong><code>pc_x</code></strong> :&ensp;<code>np.array</code></dt>





  
  

  302
  
<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>





  
  

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<dt><strong><code>method</code></strong> :&ensp;<code>string</code>, optional</dt>





  
  

  304
  
<dd>'mean', 'modified_mean', 'map', or 'modified_map'.</dd>





  
  

  305
  
<dt><strong><code>thres</code></strong> :&ensp;<code>float</code>, optional</dt>





  
  

  306
  
<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&lt;thres</span><script type="math/tex">(n_{i}+n_{j}+e_{ij})/N<thres</script></span>, only applied to mean method.</dd>





  
  

  307
  
</dl>





  
  

  308
  
<h2 id="retruns">Retruns</h2>





  
  

  309
  
<p>G : nx.Graph





  
  

  310
  
The graph of edge scores.</p></div>





  
  

  311
  
</dd>





  
  

  312
  
<dt id="VITAE.inference.Inferer.modify_wtilde"><code class="name flex">





  
  

  313
  
<span>def <span class="ident">modify_wtilde</span></span>(<span>self, w_tilde, edges)</span>





  
  

  314
  
</code></dt>





  
  

  315
  
<dd>





  
  

  316
  
<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>





  
  

  317
  
<h2 id="parameters">Parameters</h2>





  
  

  318
  
<dl>





  
  

  319
  
<dt><strong><code>w_tilde</code></strong> :&ensp;<code>np.array</code></dt>





  
  

  320
  
<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>





  
  

  321
  
<dt><strong><code>edges</code></strong> :&ensp;<code>np.array</code></dt>





  
  

  322
  
<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>





  
  

  323
  
</dl>





  
  

  324
  
<h2 id="retruns">Retruns</h2>





  
  

  325
  
<p>w : np.array





  
  

  326
  
The projected <span><span class="MathJax_Preview">\tilde{w}</span><script type="math/tex">\tilde{w}</script></span>.</p></div>





  
  

  327
  
</dd>





  
  

  328
  
<dt id="VITAE.inference.Inferer.build_milestone_net"><code class="name flex">





  
  

  329
  
<span>def <span class="ident">build_milestone_net</span></span>(<span>self, subgraph, init_node: int)</span>





  
  

  330
  
</code></dt>





  
  

  331
  
<dd>





  
  

  332
  
<div class="desc"><p>Build the milestone network.</p>





  
  

  333
  
<h2 id="parameters">Parameters</h2>





  
  

  334
  
<dl>





  
  

  335
  
<dt><strong><code>subgraph</code></strong> :&ensp;<code>nx.Graph</code></dt>





  
  

  336
  
<dd>The connected component of the backbone given the root vertex.</dd>





  
  

  337
  
<dt><strong><code>init_node</code></strong> :&ensp;<code>int</code></dt>





  
  

  338
  
<dd>The root vertex.</dd>





  
  

  339
  
</dl>





  
  

  340
  
<h2 id="returns">Returns</h2>





  
  

  341
  
<dl>





  
  

  342
  
<dt><strong><code>df_subgraph</code></strong> :&ensp;<code>pd.DataFrame </code></dt>





  
  

  343
  
<dd>The milestone network.</dd>





  
  

  344
  
</dl></div>





  
  

  345
  
</dd>





  
  

  346
  
<dt id="VITAE.inference.Inferer.comp_pseudotime"><code class="name flex">





  
  

  347
  
<span>def <span class="ident">comp_pseudotime</span></span>(<span>self, milestone_net, init_node: int, w)</span>





  
  

  348
  
</code></dt>





  
  

  349
  
<dd>





  
  

  350
  
<div class="desc"><p>Compute pseudotime.</p>





  
  

  351
  
<h2 id="parameters">Parameters</h2>





  
  

  352
  
<dl>





  
  

  353
  
<dt><strong><code>milestone_net</code></strong> :&ensp;<code>pd.DataFrame</code></dt>





  
  

  354
  
<dd>The milestone network.</dd>





  
  

  355
  
<dt><strong><code>init_node</code></strong> :&ensp;<code>int</code></dt>





  
  

  356
  
<dd>The root vertex.</dd>





  
  

  357
  
<dt><strong><code>w</code></strong> :&ensp;<code>np.array</code></dt>





  
  

  358
  
<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>





  
  

  359
  
</dl>





  
  

  360
  
<h2 id="returns">Returns</h2>





  
  

  361
  
<dl>





  
  

  362
  
<dt><strong><code>pseudotime</code></strong> :&ensp;<code>np.array</code></dt>





  
  

  363
  
<dd><span><span class="MathJax_Preview">[N, k]</span><script type="math/tex">[N, k]</script></span> The estimated pseudtotime.</dd>





  
  

  364
  
</dl></div>





  
  

  365
  
</dd>





  
  

  366
  
</dl>





  
  

  367
  
</dd>





  
  

  368
  
</dl>





  
  

  369
  
</section>





  
  

  370
  
</article>





  
  

  371
  
<nav id="sidebar">





  
  

  372
  
<div class="toc">





  
  

  373
  
<ul></ul>





  
  

  374
  
</div>





  
  

  375
  
<ul id="index">





  
  

  376
  
<li><h3>Super-module</h3>





  
  

  377
  
<ul>





  
  

  378
  
<li><code><a title="VITAE" href="index.html">VITAE</a></code></li>





  
  

  379
  
</ul>





  
  

  380
  
</li>





  
  

  381
  
<li><h3><a href="#header-classes">Classes</a></h3>





  
  

  382
  
<ul>





  
  

  383
  
<li>





  
  

  384
  
<h4><code><a title="VITAE.inference.Inferer" href="#VITAE.inference.Inferer">Inferer</a></code></h4>





  
  

  385
  
<ul class="">





  
  

  386
  
<li><code><a title="VITAE.inference.Inferer.build_graphs" href="#VITAE.inference.Inferer.build_graphs">build_graphs</a></code></li>





  
  

  387
  
<li><code><a title="VITAE.inference.Inferer.modify_wtilde" href="#VITAE.inference.Inferer.modify_wtilde">modify_wtilde</a></code></li>





  
  

  388
  
<li><code><a title="VITAE.inference.Inferer.build_milestone_net" href="#VITAE.inference.Inferer.build_milestone_net">build_milestone_net</a></code></li>





  
  

  389
  
<li><code><a title="VITAE.inference.Inferer.comp_pseudotime" href="#VITAE.inference.Inferer.comp_pseudotime">comp_pseudotime</a></code></li>





  
  

  390
  
</ul>





  
  

  391
  
</li>





  
  

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</ul>





  
  

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