add root cause localization transformer

docs/api-reference/time-series-root-cause-localization.md

@@ -0,0 +1,49 @@
+At Mircosoft, we develop a decision tree based root cause localization method which helps to find out the root causes for an anomaly incident at a specific timestamp incrementally. 
+
+## Multi-Dimensional Root Cause Localization
+It's a common case that one measure is collected with many dimensions (*e.g.*, Province, ISP) whose values are categorical(*e.g.*, Beijing or Shanghai for dimension Province). When a measure's value deviates from its expected value, this measure encounters anomalies. In such case, operators would like to localize the root cause dimension combinations rapidly and accurately. Multi-dimensional root cause localization is critical to troubleshoot and mitigate such case.
+
+## Algorithm
+
+The decision tree based root cause localization method is unsupervised, which means training step is not needed. It consists of the following major steps:
+
+(1) Find the best dimension which divides the anomalous and regular data based on decision tree according to entropy gain and entropy gain ratio.
+
+(2) Find the top anomaly points which contribute the most to anomaly incident given the selected best dimension.
+
+### Decision Tree
+
+[Decision tree](https://en.wikipedia.org/wiki/Decision_tree) algorithm chooses the highest information gain to split or construct a decision tree.  We use it to choose the dimension which contributes the most to the anomaly. Following are some concepts used in decision tree.
+
+#### Information Entropy
+
+Information [entropy](https://en.wikipedia.org/wiki/Entropy_(information_theory)) is a measure of disorder or uncertainty. You can think of it as a measure of purity as well. The less the value , the more pure of data D.
+
+$$Ent(D) = - \sum_{k=1}^{|y|}  p_k\log_2(p_k) $$
+
+where $p_k$ represents the probability of an element in dataset. In our case, there are only two classes, the anomalous points and the regular points.  $|y|$ is the count of total anomalies.
+
+#### Information Gain
+[Information gain](https://en.wikipedia.org/wiki/Information_gain_in_decision_trees) is a metric to measure the reduction of this disorder in our target class given additional information about it. Mathematically it can be written as:
+
+$$Gain(D, a) = Ent(D) - \sum_{v=1}^{|V|} \frac{|D^V|}{|D |} Ent(D^v) $$
+
+Where $Ent(D^v)$ is the entropy of set points in D for which dimension $a$ is equal to $v$, $|D|$ is the total number of points in dataset $D$.  $|D^V|$ is the total number of points in dataset $D$ for which dimension $a$ is equal to $v$.
+
+For all aggregated dimensions, we calculate the information for each dimension. The greater the reduction in this uncertainty, the more information is gained about D from dimension $a$.
+
+#### Entropy Gain Ratio
+
+Information gain is biased toward variables with large number of distinct values. A modification is [information gain ratio](https://en.wikipedia.org/wiki/Information_gain_ratio), which reduces its bias.
+
+$$Ratio(D, a) = \frac{Gain(D,a)} {IV(a)} $$
+
+where intrinsic value($IV$) is the entropy of split (with respect to dimension $a$ on focus).
+
+$$IV(a) = -\sum_{v=1}^V\frac{|D^v|} {|D|} \log_2 \frac{|D^v|} {|D|}  $$
+
+In our strategy, firstly, for all the aggregated dimensions, we loop the dimension to find the dimension whose entropy gain is above mean entropy gain, then from the filtered dimensions,  we select the dimension with highest entropy ratio as the best dimension. In the meanwhile, dimensions for which the anomaly value count is only one, we include it when calculation.
+
+> [!Note]
+> 1. As our algorithm depends on the data you input, so if the input points is incorrect or incomplete, the calculated result will be unexpected. 
+> 2. Currently, the algorithm localize the root cause incrementally, which means at most one dimension with the values are detected. If you want to find out all the dimensions that contribute to the anomaly, you can call this API recursively by updating the anomaly incident with the fixed dimension value.

docs/api-reference/time-series-root-cause-surprise-score.md

@@ -0,0 +1,6 @@
+Surprise score is used to capture the relative change for the root cause item.
+$$S_i(m) = 0.5(  p_i\log_2(\frac{2p_i} {p_i+q_i}) + q_i \log_2(\frac{2q_i}{p_i+q_i}) )$$
+$$p_i(m)= \frac{F_i(m)} {F(m)} $$
+$$q_i(m)= \frac{A_i(m)} {A(m)} $$
+where $F_i$ is the forecasted value for root cause item $i$,  $A_i$ is the actual value for root cause item $i$, $F$ is the forecasted value for the anomly point and  $A$ is the actual value for anomaly point.
+For details of the surprise score, refer to [this document](https://www.usenix.org/system/files/conference/nsdi14/nsdi14-paper-bhagwan.pdf)

docs/samples/Microsoft.ML.Samples/Dynamic/Transforms/TimeSeries/LocalizeRootCause.cs

@@ -0,0 +1,113 @@
+using System;
+using System.Collections.Generic;
+using Microsoft.ML;
+using Microsoft.ML.TimeSeries;
+
+namespace Samples.Dynamic
+{
+    public static class LocalizeRootCause
+    {
+        private static string AGG_SYMBOL = "##SUM##";
+        public static void Example()
+        {
+            // Create a new ML context, for ML.NET operations. It can be used for
+            // exception tracking and logging, as well as the source of randomness.
+            var mlContext = new MLContext();
+
+            // Create an root cause localizatin input instance.
+            DateTime timestamp = GetTimestamp();
+            var data = new RootCauseLocalizationInput(timestamp, GetAnomalyDimension(), new List<MetricSlice>() { new MetricSlice(timestamp, GetPoints()) }, AggregateType.Sum, AGG_SYMBOL);
+
+            // Get the root cause localization result
+            RootCause prediction = mlContext.AnomalyDetection.LocalizeRootCause(data);
+
+            // Print the localization result.
+            int count = 0;
+            foreach (RootCauseItem item in prediction.Items)
+            {
+                count++;
+                Console.WriteLine($"Root cause item #{count} ...");
+                Console.WriteLine($"Score: {item.Score}, Path: {String.Join(" ",item.Path)}, Direction: {item.Direction}, Dimension:{String.Join(" ", item.Dimension)}");
+            }
+
+            //Item #1 ...
+            //Score: 0.26670448876705927, Path: DataCenter, Direction: Up, Dimension:[Country, UK] [DeviceType, ##SUM##] [DataCenter, DC1]
+        }
+
+        private static List<Point> GetPoints()
+        {
+            List<Point> points = new List<Point>();
+
+            Dictionary<string, Object> dic1 = new Dictionary<string, Object>();
+            dic1.Add("Country", "UK");
+            dic1.Add("DeviceType", "Laptop");
+            dic1.Add("DataCenter", "DC1");
+            points.Add(new Point(200, 100, true, dic1));
+
+            Dictionary<string, Object> dic2 = new Dictionary<string, Object>();
+            dic2.Add("Country", "UK");
+            dic2.Add("DeviceType", "Mobile");
+            dic2.Add("DataCenter", "DC1");
+            points.Add(new Point(1000, 100, true, dic2));
+
+            Dictionary<string, Object> dic3 = new Dictionary<string, Object>();
+            dic3.Add("Country", "UK");
+            dic3.Add("DeviceType", AGG_SYMBOL);
+            dic3.Add("DataCenter", "DC1");
+            points.Add(new Point(1200, 200, true, dic3));
+
+            Dictionary<string, Object> dic4 = new Dictionary<string, Object>();
+            dic4.Add("Country", "UK");
+            dic4.Add("DeviceType", "Laptop");
+            dic4.Add("DataCenter", "DC2");
+            points.Add(new Point(100, 100, false, dic4));
+
+            Dictionary<string, Object> dic5 = new Dictionary<string, Object>();
+            dic5.Add("Country", "UK");
+            dic5.Add("DeviceType", "Mobile");
+            dic5.Add("DataCenter", "DC2");
+            points.Add(new Point(200, 200, false, dic5));
+
+            Dictionary<string, Object> dic6 = new Dictionary<string, Object>();
+            dic6.Add("Country", "UK");
+            dic6.Add("DeviceType", AGG_SYMBOL);
+            dic6.Add("DataCenter", "DC2");
+            points.Add(new Point(300, 300, false, dic6));
+
+            Dictionary<string, Object> dic7 = new Dictionary<string, Object>();
+            dic7.Add("Country", "UK");
+            dic7.Add("DeviceType", AGG_SYMBOL);
+            dic7.Add("DataCenter", AGG_SYMBOL);
+            points.Add(new Point(1500, 500, true, dic7));
+
+            Dictionary<string, Object> dic8 = new Dictionary<string, Object>();
+            dic8.Add("Country", "UK");
+            dic8.Add("DeviceType", "Laptop");
+            dic8.Add("DataCenter", AGG_SYMBOL);
+            points.Add(new Point(300, 200, true, dic8));
+
+            Dictionary<string, Object> dic9 = new Dictionary<string, Object>();
+            dic9.Add("Country", "UK");
+            dic9.Add("DeviceType", "Mobile");
+            dic9.Add("DataCenter", AGG_SYMBOL);
+            points.Add(new Point(1200, 300, true, dic9));
+
+            return points;
+        }
+
+        private static Dictionary<string, Object> GetAnomalyDimension()
+        {
+            Dictionary<string, Object> dim = new Dictionary<string, Object>();
+            dim.Add("Country", "UK");
+            dim.Add("DeviceType", AGG_SYMBOL);
+            dim.Add("DataCenter", AGG_SYMBOL);
+
+            return dim;
+        }
+
+        private static DateTime GetTimestamp()
+        {
+            return new DateTime(2020, 3, 23, 0, 0, 0);
+        }
+    }
+}

src/Microsoft.ML.TimeSeries/ExtensionsCatalog.cs

@@ -2,7 +2,10 @@
 // The .NET Foundation licenses this file to you under the MIT license.
 // See the LICENSE file in the project root for more information.
 
+using System;
+using System.Reflection;
 using Microsoft.ML.Data;
+using Microsoft.ML.TimeSeries;
 using Microsoft.ML.Transforms.TimeSeries;
 
 namespace Microsoft.ML
@@ -143,9 +146,59 @@ public static SsaSpikeEstimator DetectSpikeBySsa(this TransformsCatalog catalog,
         /// </format>
         /// </example>
         public static SrCnnAnomalyEstimator DetectAnomalyBySrCnn(this TransformsCatalog catalog, string outputColumnName, string inputColumnName,
-            int windowSize=64, int backAddWindowSize=5, int lookaheadWindowSize=5, int averageingWindowSize=3, int judgementWindowSize=21, double threshold=0.3)
+            int windowSize = 64, int backAddWindowSize = 5, int lookaheadWindowSize = 5, int averageingWindowSize = 3, int judgementWindowSize = 21, double threshold = 0.3)
             => new SrCnnAnomalyEstimator(CatalogUtils.GetEnvironment(catalog), outputColumnName, windowSize, backAddWindowSize, lookaheadWindowSize, averageingWindowSize, judgementWindowSize, threshold, inputColumnName);
 
+        /// <summary>
+        /// Create <see cref="RootCause"/>, which localizes root causes using decision tree algorithm.
+        /// </summary>
+        /// <param name="catalog">The anomaly detection catalog.</param>
+        /// <param name="src">Root cause's input. The data is an instance of <see cref="Microsoft.ML.TimeSeries.RootCauseLocalizationInput"/>.</param>
+        /// <param name="beta">Beta is a weight parameter for user to choose. It is used when score is calculated for each root cause item. The range of beta should be in [0,1]. For a larger beta, root cause point which has a large difference between value and expected value will get a high score. On the contrary, for a small beta, root cause items which has a high relative change will get a high score.</param>
+        /// <example>
+        /// <format type="text/markdown">
+        /// <![CDATA[
+        /// [!code-csharp[LocalizeRootCause](~/../docs/samples/docs/samples/Microsoft.ML.Samples/Dynamic/Transforms/TimeSeries/LocalizeRootCause.cs)]
+        /// ]]>
+        /// </format>
+        /// </example>
+        public static RootCause LocalizeRootCause(this AnomalyDetectionCatalog catalog, RootCauseLocalizationInput src, double beta = 0.5)
+        {
+            //check the root cause input
+            CheckRootCauseInput(src);
+
+            //check beta
+            if (beta < 0 || beta > 1) {
+                throw new ArgumentException("Beta must be in [0,1]");
+            }
+
+            //find out the root cause
+            RootCauseAnalyzer analyzer = new RootCauseAnalyzer(src, beta);
+            RootCause dst  = analyzer.Analyze();
+            return dst;
+        }
+
+        private static void CheckRootCauseInput(RootCauseLocalizationInput src)
+        {
+            if (src.Slices.Count < 1)
+            {
+                throw new ArgumentException("Length of Slices must be larger than 0");
+            }
+
+            bool containsAnomalyTimestamp = false;
+            foreach (MetricSlice slice in src.Slices)
+            {
+                if (slice.TimeStamp.Equals(src.AnomalyTimestamp))
+                {
+                    containsAnomalyTimestamp = true;
+                }
+            }
+            if (!containsAnomalyTimestamp)
+            {
+                throw new ArgumentException("Has no points in the given anomaly timestamp");
+            }
+        }
+
         /// <summary>
         /// Singular Spectrum Analysis (SSA) model for univariate time-series forecasting.
         /// For the details of the model, refer to http://arxiv.org/pdf/1206.6910.pdf.