A.1 Conditional MSE of the treatment effect estimator The expression for the conditional mean squared error used in Section 2 can be derived as follows. 's as the only source of randomness in the above expression and assuming that they are Abadie et al., 2010), or the assumption that treatment periods are themselves chosen at random and In this section we present the exact mixed-integer programming formulations that can be used for solving the proposed models in one of the available academic or commercial solvers. SCIP (Gamrath et al., 2020) which can handle mixed-integer nonlinear programs (MINLP's) with We need two additional observations to formulate the problem as a quadratic objective with linear constraints. 's can be carried inside the The problem becomes more complicated when there is no constraint on the number of treated units. In this section we provide a proof of Theorem 1. A B null which is independent of the index l .

The position and the orientation of a rigid body object pushed by a robot on a planar surface are extremely difficult to predict. In this paper, the prediction problem is formulated as a disturbance observer design problem. The disturbance observer provides accurate estimation of the total sum of model errors and external disturbances acting on the object. From the estimation results, it is revealed that there is a strong linear relationship between the applied force or torque and the estimated disturbances. The proposed prediction algorithm has two phases: the identification & the prediction. During the identification phase, the linear relationship is identified from the observer output using a recursive least-square algorithm. In the prediction phase, the identified linear relationship is used with a force plan, which would be provided by a mission planner, to predict the position and the orientation of an object. The algorithm is tested for six different push experimental data available from the MIT MCube Lab. The proposed algorithm shows improved performance in reducing the prediction error compared to a simple correction algorithm.

The softmax activation is something like the combination of the multiple sigmoid functions. It is used to ensure that the total sum of the output from the layer is equal to 100%. For example, in multi-class classification problems where every observation belongs to exactly one class. So, here is the difference with Sigmoid: the first one allows the inputs/observations to belong to many classes. This activation may be placed in the final layer of the convolutional neural network (CNN) to classify the classes of hand-written digits (from 0 to 9).

Identifying a set of homogeneous clusters in a heterogeneous dataset is one of the most important classes of problems in statistical modeling. In the realm of unsupervised partitional clustering, k-means is a very important algorithm for this. In this technical report, we develop a new k-means variant called Augmented k-means, which is a hybrid of k-means and logistic regression. During each iteration, logistic regression is used to predict the current cluster labels, and the cluster belonging probabilities are used to control the subsequent re-estimation of cluster means. Observations which can't be firmly identified into clusters are excluded from the re-estimation step. This can be valuable when the data exhibit many characteristics of real datasets such as heterogeneity, non-sphericity, substantial overlap, and high scatter. Augmented k-means frequently outperforms k-means by more accurately classifying observations into known clusters and / or converging in fewer iterations. We demonstrate this on both simulated and real datasets. Our algorithm is implemented in Python and will be available with this report.

Facebook is making it easier for users to split a dinner bill or chip in on a group gift. The social media giant is expanding its peer-to-peer payments on Messenger, letting its US users send or receive money between groups of people. Starting with Android and desktop, the new feature will be free to use, but just like the original version, it will only support Visa or Mastercard debit cards for now. Facebook is expanding its peer-to-peer payments on Messenger, letting users send or receive money between groups of people.Users choose who they want included in the group payment and enter the amount per person or the total sum to divide evenly Tap on the plus sign in the bottom left hand corner of a group conversation to find more features, and tap the payments icon ($). Then choose anyone in the group you would like to send or request funds from and enter the amount per person or the total sum to divide evenly.

Data clustering is an important area of data mining. This is an unsupervised study where data of similar types are put into one cluster while data of another types are put into different cluster. Fuzzy C means is a very important clustering technique based on fuzzy logic. Also we have some hard clustering techniques available like K-means among the popular ones. In this paper a comparative study is done between Fuzzy clustering algorithm and hard clustering algorithm