Abstract: Methods and systems for inferring data to supplement an input utilizing a neural network, and training such a system, are disclosed. In embodiments, an input is received from a sensor at the neural network. Iterations of approximate probabilities can be determined based on hidden-to-hidden Markov random field (MRF) potentials, observed-to-hidden MRF potentials, and unary MRF potentials. A constant can be identified using a root-finding algorithm. The iterations can continue until convergence. The final iteration of the approximate probability can be used to supplement the input to produce an output.

Abstract: A digital ad-buying platform uses counterfactual-based incrementality measurement by implementing randomization and/or a correction for auction win bias to avoid the need to identify counterfactual winner types in the control group. This approach can estimate impact at the individual consumer level. Confidence levels can be determined using Gibbs sampling in the context of causal analysis in the presence of non-compliance.

Abstract: A system for training a neural work that includes an input interface for accessing input data for the neural network and a processor in communication with the input interface. The processor is programmed to receive input at the neural network and output a trained neural networking utilizing a forward prorogation and a backward propagation, wherein the forward propagation includes utilizing a root-finding procedure to identify a fixed point associated with one or more parameters of the neural network, wherein the backward propagation includes identifying a derivative of a loss associated with the parameters of the network.

Abstract: A digital ad-buying platform uses counterfactual-based incrementality measurement by implementing randomization and/or a correction for auction win bias to avoid the need to identify counterfactual winner types in the control group. This approach can estimate impact at the individual consumer level. Confidence levels can be determined using Gibbs sampling in the context of causal analysis in the presence of non-compliance.

Abstract: A digital ad-buying platform uses counterfactual-based incrementality measurement by implementing randomization and/or a correction for auction win bias to avoid the need to identify counterfactual winner types in the control group. This approach can estimate impact at the individual consumer level. Confidence levels can be determined using Gibbs sampling in the context of causal analysis in the presence of non-compliance.

Abstract: A digital ad-buying platform uses counterfactual-based incrementality measurement by implementing randomization and/or a correction for auction win bias to avoid the need to identify counterfactual winner types in the control group. This approach can estimate impact at the individual consumer level. Confidence levels can be determined using Gibbs sampling in the context of causal analysis in the presence of non-compliance.

Abstract: A system for training a neural work that includes an input interface for accessing input data for the neural network and a processor in communication with the input interface. The processor is programmed to receive input at the neural network and output a trained neural networking utilizing a forward prorogation and a backward propagation, wherein the forward propagation includes utilizing a root-finding procedure to identify a fixed point associated with one or more parameters of the neural network, wherein the backward propagation includes identifying a derivative of a loss associated with the parameters of the network.

Abstract: A digital ad-buying platform uses counterfactual-based incrementality measurement by implementing randomization and/or a correction for auction win bias to avoid the need to identify counterfactual winner types in the control group. This approach can estimate impact at the individual consumer level. Confidence levels can be determined using Gibbs sampling in the context of causal analysis in the presence of non-compliance.

Abstract: A digital ad-buying platform uses counterfactual-based incrementality measurement by implementing randomization and/or a correction for auction win bias to avoid the need to identify counterfactual winner types in the control group. This approach can estimate impact at the individual consumer level. Confidence levels can be determined using Gibbs sampling in the context of causal analysis in the presence of non-compliance.

Abstract: A digital ad-buying platform uses counterfactual-based incrementality measurement by implementing randomization and/or a correction for auction win bias to avoid the need to identify counterfactual winner types in the control group. This approach can estimate impact at the individual consumer level. Confidence levels can be determined using Gibbs sampling in the context of causal analysis in the presence of non-compliance.

Abstract: A digital ad-buying platform uses counterfactual-based incrementality measurement by implementing randomization and/or a correction for auction win bias to avoid the need to identify counterfactual winner types in the control group. This approach can estimate impact at the individual consumer level. Confidence levels can be determined using Gibbs sampling in the context of causal analysis in the presence of non-compliance.