Abstract: Aspects of the subject technology provide for training a machine learning model based on data from a healthy cohort of study participants. The machine learning model can be used to predict an age of a user based on physiological sensor data and determine a biological age of a user. An age gap can be determined between the user's chronological age and biological age and a notification or recommendation made to the user based on the age gap. An age gap rate of change can be made across multiple age gap determinations.

Abstract: The subject technology provides for large-scale training of foundation models for physiological signals from wearable electronic devices. An apparatus receives receive input data having a plurality of physiological signal information segments associated with a user. The apparatus applies one or more augmentation functions to the plurality of physiological signal information segments to generate an augmented version of the plurality of physiological signal information segments. The apparatus trains a neural network to produce a trained machine learning model by generating, via an encoder, an embedding of the augmented version having a first number of dimensions in an embedding space. The apparatus maps, via a multilayer perceptron projection, the embedding into a representation having a second number of dimensions. The apparatus determines mutual information between a pair of representations of the augmented version.

Abstract: A computing device computes a weight matrix to compute a predicted value. For each of a plurality of related tasks, an augmented observation matrix, a plug-in autocovariance matrix, and a plug-in covariance vector are computed. A weight matrix used to predict the characteristic for each of a plurality of variables and each of a plurality of related tasks is computed. (a) and (b) are repeated with the computed updated weight matrix as the computed weight matrix until a convergence criterion is satisfied: (a) a gradient descent matrix is computed using the computed plug-in autocovariance matrix, the computed plug-in covariance vector, the computed weight matrix, and a predefined relationship matrix, wherein the predefined relationship matrix defines a relationship between the plurality of related tasks, and (b) an updated weight matrix is computed using the computed gradient descent matrix.

Abstract: A computing device computes a weight matrix to compute a predicted value. For each of a plurality of related tasks, an augmented observation matrix, a plug-in autocovariance matrix, and a plug-in covariance vector are computed. A weight matrix used to predict the characteristic for each of a plurality of variables and each of a plurality of related tasks is computed. (a) and (b) are repeated with the computed updated weight matrix as the computed weight matrix until a convergence criterion is satisfied: (a) a gradient descent matrix is computed using the computed plug-in autocovariance matrix, the computed plug-in covariance vector, the computed weight matrix, and a predefined relationship matrix, wherein the predefined relationship matrix defines a relationship between the plurality of related tasks, and (b) an updated weight matrix is computed using the computed gradient descent matrix.

Abstract: A computing device computes a weight matrix to predict a value for a characteristic in a scoring dataset. For each of a plurality of related tasks, an augmented observation matrix, a plug-in autocovariance matrix, and a plug-in covariance vector are computed. A weight matrix used to predict the characteristic for each of a plurality of variables and each of a plurality of related tasks is computed. (a) and (b) are repeated with the computed updated weight matrix as the computed weight matrix until a convergence criterion is satisfied: (a) a gradient descent matrix is computed using the computed plug-in autocovariance matrix, the computed plug-in covariance vector, the computed weight matrix, and a predefined relationship matrix, wherein the predefined relationship matrix defines a relationship between the plurality of related tasks, and (b) an updated weight matrix is computed using the computed gradient descent matrix.

Abstract: A computing device updates an estimate of one or more principal components for a next observation vector. An initial observation matrix is defined with first observation vectors. A number of the first observation vectors is a predefined window length. Each observation vector of the first observation vectors includes a plurality of values. A principal components decomposition is computed using the initial observation matrix. The principal components decomposition includes a sparse noise vector s, a first singular value decomposition vector U, and a second singular value decomposition vector v for each observation vector of the first observation vectors. A rank r is determined based on the principal components decomposition. A next principal components decomposition is computed for a next observation vector using the determined rank r. The next principal components decomposition is output for the next observation vector and monitored to determine a status of a physical object.

Abstract: A computing device detects an abnormal observation vector using a principal components decomposition. The principal components decomposition includes a sparse noise vector st computed for the observation vector that includes a plurality of values, wherein each value is associated with a variable to define a plurality of variables. The sparse noise vector st has a dimension equal to m a number of the plurality of variables. A zero counter time series value ?t is computed using ?t=?i=1mst[i]. A probability value for ?t is computed using p=?i=?t+1m+1Hc[i]/?i=0m+1Hc[i], where Hc[i] includes a count of a number of times each value of ?t occurred for previous observation vectors. The probability value is compared with a predefined abnormal observation probability value. An abnormal observation indicator is set when the probability value indicates the observation vector is abnormal. The observation vector is output when the probability value indicates the observation vector is abnormal.

Abstract: A computing device computes a weight matrix to predict a value for a characteristic in a scoring dataset. For each of a plurality of related tasks, an augmented observation matrix, a plug-in autocovariance matrix, and a plug-in covariance vector are computed. A weight matrix used to predict the characteristic for each of a plurality of variables and each of a plurality of related tasks is computed. (a) and (b) are repeated with the computed updated weight matrix as the computed weight matrix until a convergence criterion is satisfied: (a) a gradient descent matrix is computed using the computed plug-in autocovariance matrix, the computed plug-in covariance vector, the computed weight matrix, and a predefined relationship matrix, wherein the predefined relationship matrix defines a relationship between the plurality of related tasks, and (b) an updated weight matrix is computed using the computed gradient descent matrix.

Abstract: A computing device detects an abnormal observation vector using a principal components decomposition. The principal components decomposition includes a sparse noise vector st computed for the observation vector that includes a plurality of values, wherein each value is associated with a variable to define a plurality of variables. The sparse noise vector st has a dimension equal to m a number of the plurality of variables. A zero counter time series value ?t is computed using ?t=?i=1mst[i]. A probability value for ?t is computed using p=?i=?t+1m+1Hc[i]/?i=0m+1Hc[i], where Hc[i] includes a count of a number of times each value of ?t occurred for previous observation vectors. The probability value is compared with a predefined abnormal observation probability value. An abnormal observation indicator is set when the probability value indicates the observation vector is abnormal. The observation vector is output when the probability value indicates the observation vector is abnormal.

Abstract: A computing device updates an estimate of one or more principal components for a next observation vector. An initial observation matrix is defined with first observation vectors. A number of the first observation vectors is a predefined window length. Each observation vector of the first observation vectors includes a plurality of values. A principal components decomposition is computed using the initial observation matrix. The principal components decomposition includes a sparse noise vector s, a first singular value decomposition vector U, and a second singular value decomposition vector ? for each observation vector of the first observation vectors. A rank r is determined based on the principal components decomposition. A next principal components decomposition is computed for a next observation vector using the determined rank r. The next principal components decomposition is output for the next observation vector and monitored to determine a status of a physical object.