Kernel Density Estimate

infoflow/entropy_kde.py

@@ -0,0 +1,86 @@
+import numpy as np
+from infoflow import multidimkde as mdkde
+from math import log
+
+
+def kerneldensityestimation(source, target, timelagx, timelagy, n, bw_coeff):
+    """
+    :param source: source time series, 1-D np.ndarray
+    :param target: target time series, 1-D np.ndarray
+    :param timelagx: time lag in x from present. Integer.
+    :param timelagy: time lag in y from present. Integer.
+    :param n: number of equally spaced points along each dimension where probabilities are to be estimated. Integer.
+    :param bw_coeff: multiplier that adjusts Gaussian bandwidth. Integer.
+    :return: transfer entropy in bits. float.
+    """
+
+    """ All code written here is based on the transfer entropy
+     toolbox, Copyright 2011 Joon Lee. Use protected under GNU."""
+
+    # fixing block lengths to 1
+    l, k = 1, 1
+
+    sourcearr = source.flatten()
+    targetarr = target.flatten()
+
+    # populating source_pat, target_pat and target_t
+    source_pat = []
+    target_pat = []
+    target_t = []
+
+    for i in range(max(l+timelagx, k+timelagy)-1, min(len(sourcearr), len(targetarr))):
+        source_pat.append(sourcearr[i - l - timelagx+1: i - timelagx+1][0])
+        target_pat.append(targetarr[i - k - timelagy+1: i - timelagy+1][0])
+        target_t.append(targetarr[i])
+
+    # reassigning to numpy arrays
+    source_pat = np.array(source_pat).reshape(len(source_pat), 1)
+    target_pat = np.array(target_pat).reshape(len(target_pat), 1)
+    target_t = np.array(target_t).reshape(len(target_t), 1)
+
+    # establishing values
+    source_pat_i = np.linspace(np.amin(source_pat) - 0.1*(np.amax(source_pat) - np.amin(source_pat)),
+                               np.amax(source_pat) + 0.1*(np.amax(source_pat) - np.amin(source_pat)), n)
+
+    target_pat_i = np.linspace(np.amin(target_pat) - 0.1*(np.amax(target_pat) - np.amin(target_pat)),
+                               np.amax(target_pat) + 0.1*(np.amax(target_pat) - np.amin(target_pat)), n)
+
+    target_t_i = np.linspace(np.amin(target_t)-0.1*(np.amax(target_t)-np.amin(target_t)),
+                            np.amax(target_t)+0.1*(np.amax(target_t)-np.amin(target_t)), n)
+
+    # reshaping the resultant arrays
+    source_pat_i = np.array(source_pat_i)
+    target_pat_i = np.array(target_pat_i)
+    target_t_i = np.array(target_t_i)
+
+    # initializing the probability density function matrix
+    pdf = np.zeros(shape=(len(target_t_i), len(source_pat_i), len(target_pat_i)))
+
+    # bookkeeping
+    source_pat = source_pat.transpose()
+    target_pat = target_pat.transpose()
+    target_t = target_t.transpose()
+
+    # populating the pdf matrix
+    x = np.vstack((source_pat, target_pat, target_t)).transpose()
+    for i in range(len(source_pat_i)):
+        for j in range(len(target_pat_i)):
+            for k in range(len(target_t_i)):
+                xi = np.hstack((source_pat_i[i], target_pat_i[j], target_t_i[k]))
+                ans = mdkde.multidimensionalkde(x, xi, bw_coeff)
+                pdf[k, i, j] = ans[0]
+
+    # normalizing probabilities
+    pdf = pdf/np.sum(pdf)
+
+    # computing transfer entropy
+    transferentropy = 0
+    for i in range(len(source_pat_i)):
+        for j in range(len(target_pat_i)):
+            for k in range(len(target_t_i)):
+                a = pdf[k, i, j]
+                b = np.sum(pdf[:, i, j])
+                c = np.sum(pdf[k, :, j])
+                d = np.sum(sum(pdf[:, :, j]))
+                transferentropy += a * log(((a * d) / (b * c)), 2)
+    return transferentropy

infoflow/multidimkde.py

@@ -0,0 +1,32 @@
+import numpy as np
+from math import pi, exp, sqrt
+
+
+def multidimensionalkde(x, xi, bw_coeff):
+    """
+    :param x: np.ndarray, rows are observations and columns are dimensions.
+    :param xi: np.ndarray, coordinates at which joint probabilities are to be estimated.
+    :param bw_coeff: multiplier that adjusts the rule of thumb bandwidth. Integer.
+    :return: joint probability at xi
+    """
+
+    # assertions to ensure input is in right format.
+    assert isinstance(x, np.ndarray)
+    assert isinstance(xi, np.ndarray)
+
+    n, d = np.shape(x)
+    # pick the bandwidth for each dimension
+    h = np.zeros(shape=(1, d))
+    for i in range(d):
+        h[0, i] = float(bw_coeff * 1.06 * n**(-1/5) *np.std(x[:, i],ddof=1))
+    # estimating probability at xi
+    p = np.zeros(shape=(np.shape(xi)[0], 1))
+    for k in range(len(p)):
+        for i in range(n):
+            prod = 1
+            for j in range(d):
+                u = float((xi[j] - x[i, j])/h[0][j])
+                prod = float(prod * 1/sqrt(2*pi) * exp(-0.5*(u**2)) / h[0][j])
+            p[k] += prod
+    p = p/n
+    return p

infoflow/tests/input_kde/entropykdeinputx.txt

@@ -0,0 +1 @@
+10.4211260079593	9.15959175116347	8.42791637961942	9.79937565892561	11.0935185821076	9.73725099429120	10.2243469322360	9.14123254116025	9.27978556360681	10.4625464979946	11.0532504912095	8.37120765662389	8.31299790562039	11.3632685729923	10.0351674383055	9.78837437910691	10.3025585944617	9.97080241324564	10.3538933865610	10.6079548361543	8.94148954012898	9.47833605650219	9.92537602561508	9.50144983292374	10.4229167707908	8.94229569585545	10.1630719263382	8.31144638274103	8.70392723628035	10.9626524057649	10.7513587129864	10.6985933029311	10.1934766837466	8.55865025366214	9.77089142787289	11.3586402663943	7.86245295803992	10.3451863308292	7.46527397614331	9.68710681121817	10.3649792158121	8.40812696263984	10.8562622100752	9.23978685343992	10.5440053605012	10.4683979739141	9.73608537929506	10.5512564821944	10.0484117707993	8.04072569129428	10.6735654913598	10.1828715200493	9.96968448112454	10.2489827369610	10.0531253810500	7.67165861107142	11.7197788310825	9.57947501239318	9.29625795552166	11.3998640005889	10.1373742414350	9.01100801303883	10.9049803732133	10.1033344160733	9.32410854469947	11.6280330977918	9.85747779740347	9.69796324352113	8.86402817842106	10.1171639601262	11.5280148529030	10.8757601216499	9.80653805805204	9.73017365115883	10.6196452989191	11.7917319631748	9.91330802847372	9.75905627047967	10.2835667875428	8.71599998475651	10.9803639476732	9.45264445714630	9.43835681862873	7.91040504493523	9.04374138942974	10.2119536137048	10.7971784055176	11.1546396794403	8.70620162412084	9.66870517734535	9.87619320128848	10.3404378591972	10.4166902669334	10.3604459390833	9.52905000082007	9.78773022225650	9.19197187636095	9.33759915410536	11.8571358650712	8.78386760180735	9.74288266411103	8.80846479929184	10.7973171856024	8.71773764110380	8.14439559714581	8.34305489301146	10.6670110210607	12.4146862141603	9.61705667616662	10.9746111393636	11.2613670851036	11.2255057655008	11.8794812760294	9.66125009841665	10.9770718448007	9.61885979100899	8.20394806363581	9.75222917260762	10.3807775239919	10.9185911679075	10.8563781321093	10.2231245103995	11.1730192468860	9.72786807833919	8.73372705809844	9.02992561801242	8.86095513474243	11.1177126097330	9.82991216438658	8.61585951453221	9.65034485444263	10.1196333015828	9.67688510208878	11.6637580508535	11.5434488090031	9.48286063156920	10.1694907154755	10.5045025708633	10.1803562858932	9.56685897211484	10.5537178614578	9.05063141544852	12.9054894272364	9.75302003682373	10.2941874860983	9.20946963016349	8.55666581778405	11.1430581055165	10.0936766601589	10.3670319086311	8.14386564486635	10.4535441133938	11.7223379926330	10.5927084785974	11.2144544492494	11.6879516780366	11.4556534338735	8.65122029311518	9.47934281204521	8.40963475436907	10.6278446404594	12.0162482623612	11.4696135507092	10.8674026057028	8.97336288741732	8.95834919952158	9.78664488766869	9.89131930266141	10.7660388327426	12.2657015270320	9.88205821947244	9.96323461539321	11.2232922459353	11.1769593227852	8.28437478168918	9.58148155918462	9.60348889503716	8.92353335913221	9.29170798438943	10.0571438414249	11.2758327997102	10.7733479413764	10.8705727179738	9.18109123035243	10.6157976774387	11.4801845404507	8.71623561375216	12.2037500514460	11.3266086901697	8.79914325310611	10.4582994211230	9.23599690280768	9.55299920735131	9.30433656337055	9.55012430373347	9.46276994556222	9.37910504539161	9.60009122456007	10.4950921294591	11.8306052926597	8.41056780343131	9.86289137162470

infoflow/tests/input_kde/entropykdeinputx1.txt

@@ -0,0 +1 @@
+10.4211260079593	9.15959175116347	8.42791637961942	9.79937565892561	11.0935185821076	9.73725099429120	10.2243469322360	9.14123254116025	9.27978556360681	10.4625464979946	11.0532504912095	8.37120765662389	8.31299790562039	11.3632685729923	10.0351674383055	9.78837437910691	10.3025585944617	9.97080241324564	10.3538933865610	10.6079548361543	8.94148954012898	9.47833605650219	9.92537602561508	9.50144983292374	10.4229167707908	8.94229569585545	10.1630719263382	8.31144638274103	8.70392723628035	10.9626524057649	10.7513587129864	10.6985933029311	10.1934766837466	8.55865025366214	9.77089142787289	11.3586402663943	7.86245295803992	10.3451863308292	7.46527397614331	9.68710681121817	10.3649792158121	8.40812696263984	10.8562622100752	9.23978685343992	10.5440053605012	10.4683979739141	9.73608537929506	10.5512564821944	10.0484117707993	8.04072569129428	10.6735654913598	10.1828715200493	9.96968448112454	10.2489827369610	10.0531253810500	7.67165861107142	11.7197788310825	9.57947501239318	9.29625795552166	11.3998640005889	10.1373742414350	9.01100801303883	10.9049803732133	10.1033344160733	9.32410854469947	11.6280330977918	9.85747779740347	9.69796324352113	8.86402817842106	10.1171639601262	11.5280148529030	10.8757601216499	9.80653805805204	9.73017365115883	10.6196452989191	11.7917319631748	9.91330802847372	9.75905627047967	10.2835667875428	8.71599998475651	10.9803639476732	9.45264445714630	9.43835681862873	7.91040504493523	9.04374138942974	10.2119536137048	10.7971784055176	11.1546396794403	8.70620162412084	9.66870517734535	9.87619320128848	10.3404378591972	10.4166902669334	10.3604459390833	9.52905000082007	9.78773022225650	9.19197187636095	9.33759915410536	11.8571358650712	8.78386760180735	9.74288266411103	8.80846479929184	10.7973171856024	8.71773764110380	8.14439559714581	8.34305489301146	10.6670110210607	12.4146862141603	9.61705667616662	10.9746111393636	11.2613670851036	11.2255057655008	11.8794812760294	9.66125009841665	10.9770718448007	9.61885979100899	8.20394806363581	9.75222917260762	10.3807775239919	10.9185911679075	10.8563781321093	10.2231245103995	11.1730192468860	9.72786807833919	8.73372705809844	9.02992561801242	8.86095513474243	11.1177126097330	9.82991216438658	8.61585951453221	9.65034485444263	10.1196333015828	9.67688510208878	11.6637580508535	11.5434488090031	9.48286063156920	10.1694907154755	10.5045025708633	10.1803562858932	9.56685897211484	10.5537178614578	9.05063141544852	12.9054894272364	9.75302003682373	10.2941874860983	9.20946963016349	8.55666581778405	11.1430581055165	10.0936766601589	10.3670319086311	8.14386564486635	10.4535441133938	11.7223379926330	10.5927084785974	11.2144544492494	11.6879516780366	11.4556534338735	8.65122029311518	9.47934281204521	8.40963475436907	10.6278446404594	12.0162482623612	11.4696135507092	10.8674026057028	8.97336288741732	8.95834919952158	9.78664488766869	9.89131930266141	10.7660388327426	12.2657015270320	9.88205821947244	9.96323461539321	11.2232922459353	11.1769593227852	8.28437478168918	9.58148155918462	9.60348889503716	8.92353335913221	9.29170798438943	10.0571438414249	11.2758327997102	10.7733479413764	10.8705727179738	9.18109123035243	10.6157976774387	11.4801845404507	8.71623561375216	12.2037500514460	11.3266086901697	8.79914325310611	10.4582994211230	9.23599690280768	9.55299920735131	9.30433656337055	9.55012430373347	9.46276994556222	9.37910504539161	9.60009122456007	10.4950921294591	11.8306052926597	8.41056780343131	9.86289137162470

infoflow/tests/input_kde/entropykdeinputx10.txt

@@ -0,0 +1 @@
+10.8699833127185	9.68443275893966	10.5474476160265	9.67150769870410	10.7441432241123	9.54103668641083	9.63948659269747	8.87017541640272	8.52449047797456	10.5632632713485	11.1222725620246	10.1693053869160	9.29632394105644	9.08850773421474	9.04290421198221	12.0122190052164	9.90985980443958	8.84689788899307	8.88867199607254	9.28736211049221	9.75906286068963	12.0711034949049	10.0237853657269	8.85450478825283	9.28631148731868	9.05245702052238	11.3083260817942	11.9225930224378	11.3635869955078	9.78374948750941	11.2840706560335	10.0387666785327	9.86887022046866	8.76961125969829	9.66746858109348	9.17092316882893	9.62967933942374	9.46861769610689	9.58077693275956	8.44574988870922	10.5462090906056	8.65154081077131	10.4052637417213	9.40559083878890	9.06690749411444	8.14427566538484	9.73898601602242	10.8774108836587	11.7096320388117	10.7186783456309	8.74706404508343	9.82932986439422	11.3610074119434	10.6392839511152	9.41261046561218	10.5054843441130	10.8199808053511	9.62344252530183	9.28095789013691	9.27298536814906	10.5082888888033	10.3242291915240	9.52174214619540	8.38617504517682	10.0890008381056	9.77536566753334	9.97716400632260	11.4930037953760	10.1230906889496	9.24997610419842	12.2525291832571	9.25516781841040	9.52884670833557	10.9540907070798	8.43651427795226	10.0381509943223	9.89605596658276	12.0771950491055	11.2850531721867	10.4428686324097	8.91364072221276	10.5478482165796	9.43442588280808	9.39819642439597	8.19561808019623	7.67083396995431	10.4020385330024	10.5473996340275	9.49313824486275	10.6522344887757	10.3631325429750	8.62523297109888	8.71135231636371	11.3145773341740	10.6427378694596	9.68452882670857	8.99675469680888	10.3312895113314	10.1723869235317	8.02483359973832	10.9645923912353	9.81285845854804	10.1280154269215	8.56214362722571	11.7281196180565	10.8134092911562	9.11178740562848	9.77150123035137	9.29994387378397	10.4798597047718	10.7740608040303	10.3319113132463	10.5207036542453	10.5506744709158	8.98411503293251	10.6865626905703	9.04885478322149	10.6280760162404	8.90290646349454	11.0863169187603	10.3839231939128	11.0239483519199	9.27226853949843	10.7962177976519	9.21947268315388	9.58929940494356	9.41243469949015	10.5439225430818	11.3974015747748	9.75220803488193	9.89411617013360	10.4888048558715	9.30453936229872	11.3832378372143	10.9727075619210	10.9032900875427	9.63238273389541	8.41996793972577	9.22065755692087	10.3025956484214	9.38350566235906	10.3223236263488	9.27343905631594	9.77293689428016	9.76923820976849	10.4758022466870	8.45789723750968	11.6985410782802	9.47610182866091	10.4343925508904	11.7175294151061	10.0356719075508	11.2214347847136	9.75811363819631	11.0376248731612	10.4131337752811	10.0757996564907	9.62930982077582	10.5059506235190	8.69429413441244	9.06679752181153	10.7464278847451	10.7566364162748	10.4964114398382	9.71242931446934	9.83630448601838	8.47298726801289	8.50357123688345	10.4700811650934	8.96711185957138	10.2816354604784	8.57760356987811	9.62884685481851	9.64703590273127	10.6296940322822	9.97453773122864	10.0339425819693	8.90393445181706	8.80722389874830	8.72291861053948	11.1723380983660	10.4304715913696	10.1669071845318	9.11065465102903	8.73348342541021	11.0315023257774	10.6366611800350	8.88094079691397	11.5910836813201	8.37013420154003	10.3667578176358	10.7998002537185	10.3338328754108	9.19997558276628	10.6557606255287	9.76975641100687	10.2326991152455	9.76774810371417	10.5360980475171	9.53935634159052	8.69901163811486	10.9110337031062

infoflow/tests/input_kde/entropykdeinputx11.txt

@@ -0,0 +1 @@
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