Forecasting with deep state space models

A computer-implemented method for using a trained machine learning model in a predictive system, comprising the following steps:

• receiving a trained deep state space model, the deep state space model including a generative model and a multi-modal inference model, wherein the generative model includes a transition model configured to describe a change of a plurality of latent states, and an emission model configured to decode the plurality of latent states to provide a plurality of synthetic observations, the deep state space model being trained by:
• a) receiving a training data set including a sequence of observation vectors each obtained at an observation step;
• for each of a plurality of observation vectors in the sequence of observation vectors, iterating b), c) and d):
• b) inferring, using the multi-modal inference model, a current latent state of the generative model by mapping a current observation vector obtained at a current observation step of the sequence of observation vectors to obtain a probability distribution of the current latent state,
• c) constructing, using the multi-modal inference model, a posterior approximation of the current latent state as a mixture density network, to yield a plurality of approximated latent state vectors,
• d) decoding, using the emission model, the plurality of approximated latent state vectors to provide a plurality of synthetic observations;
• and
• e) outputting the trained deep state space model;
• receiving an input sequence of observation vectors each obtained at an observation step;
• predicting at least one continuation of the input sequence of observation vectors, using the trained deep state space model, wherein the continuation includes a synthetic observation obtained from the trained deep state space model;
• and
• outputting the at least one continuation of the input sequence of observation vectors.

An apparatus configured to train a deep state space model using machine learning, comprising:

• an input interface;
• a memory;
• a processor;
• and
• an output interface;
• wherein the input interface is configured to receive a training data set including a sequence of observation vectors each obtained at an observation step;
• wherein the processor is configured to execute a deep state space model including a generative model and a multi-modal inference model, wherein, in use, the generative model further includes a transition model configured to describe a change of a plurality of latent states, and an emission model configured to decode the plurality of latent states to provide thereby a plurality of synthetic observations;
• wherein the processor is further configured, for a plurality of observation vectors comprised in the sequence of observation vectors, to iterate (a) inference, using the multi-modal inference model, of a current latent state of the generative model by mapping a current observation vector obtained at a current observation step of the sequence of observation vectors to obtain a probability distribution of the current latent state, and (b) construction, using the multi-modal inference model, of a posterior approximation of the current latent state as a mixture density network, to yield a plurality of approximated latent state vectors, and for a plurality of observation vectors in the sequence of observation vectors, the processor is configured to decode, using the emission model, the plurality of approximated latent state vectors to provide thereby a plurality of synthetic observations;
• and
• wherein the output interface is configured to output the trained deep state space model.

A non-transitory computer readable medium on which is stored a computer program element including a program for training a deep state space model using machine learning, the deep state space model including a generative model and a multi-modal inference model, wherein the generative model includes a transition model configured to describe a change of a plurality of latent states, and an emission model configured to decode the plurality of latent states to provide a plurality of synthetic observations, the program, when executed by a computer, causing the computer to perform the following steps:

• a) receiving a training data set including a sequence of observation vectors each obtained at an observation step;
• for each of a plurality of observation vectors in the sequence of observation vectors, iterating b), c) and d):
• b) inferring, using the multi-modal inference model, a current latent state of the generative model by mapping a current observation vector obtained at a current observation step of the sequence of observation vectors to obtain a probability distribution of the current latent state,
• c) constructing, using the multi-modal inference model, a posterior approximation of the current latent state as a mixture density network, to yield a plurality of approximated latent state vectors,
• d) decoding, using the emission model, the plurality of approximated latent state vectors to provide a plurality of synthetic observations;
• and
• e) outputting the trained deep state space model.

A non-transitory computer readable medium on which is stored a computer program element including trained model data defining a deep state space model, the deep state model including a generative model and a multi-modal inference model, wherein the generative model includes a transition model configured to describe a change of a plurality of latent states, and an emission model configured to decode the plurality of latent states to provide a plurality of synthetic observations, the trained model data being generated by a computer performing the following steps:

• a) receiving a training data set including a sequence of observation vectors each obtained at an observation step;
• for each of a plurality of observation vectors in the sequence of observation vectors, iterating b), c) and d):
• b) inferring, using the multi-modal inference model, a current latent state of the generative model by mapping a current observation vector obtained at a current observation step of the sequence of observation vectors to obtain a probability distribution of the current latent state,
• c) constructing, using the multi-modal inference model, a posterior approximation of the current latent state as a mixture density network, to yield a plurality of approximated latent state vectors,
• d) decoding, using the emission model, the plurality of approximated latent state vectors to provide a plurality of synthetic observations;
• and
• e) outputting the trained deep state space model.

A vehicle, comprising:

• a controller configured, at least partially, using a deep state space model, the deep state space model including a generative model and a multi-modal inference model, wherein the generative model includes a transition model configured to describe a change of a plurality of latent states, and an emission model configured to decode the plurality of latent states to provide a plurality of synthetic observations, the deep state space model being trained by:
• a) receiving a training data set including a sequence of observation vectors each obtained at an observation step;
• for each of a plurality of observation vectors in the sequence of observation vectors, iterating b), c) and d):
• b) inferring, using the multi-modal inference model, a current latent state of the generative model by mapping a current observation vector obtained at a current observation step of the sequence of observation vectors to obtain a probability distribution of the current latent state,
• c) constructing, using the multi-modal inference model, a posterior approximation of the current latent state as a mixture density network, to yield a plurality of approximated latent state vectors,
• d) decoding, using the emission model, the plurality of approximated latent state vectors to provide a plurality of synthetic observations;
• and
• e) outputting the trained deep state space model;
• wherein the training data set includes a sequence of observation vectors describing one or more of:
• battery state of health, or an external traffic, or a route model, or a driver behaviour model, or an engine model.

A wireless base station and/or handset, comprising:

• a controller configured, at least partially, using a deep state space model, the deep state space model including a generative model and a multi-modal inference model, wherein the generative model includes a transition model configured to describe a change of a plurality of latent states, and an emission model configured to decode the plurality of latent states to provide a plurality of synthetic observations, the deep state space model being trained by:
• a) receiving a training data set including a sequence of observation vectors each obtained at an observation step;
• for each of a plurality of observation vectors in the sequence of observation vectors, iterating b), c) and d):
• b) inferring, using the multi-modal inference model, a current latent state of the generative model by mapping a current observation vector obtained at a current observation step of the sequence of observation vectors to obtain a probability distribution of the current latent state,
• c) constructing, using the multi-modal inference model, a posterior approximation of the current latent state as a mixture density network, to yield a plurality of approximated latent state vectors,
• d) decoding, using the emission model, the plurality of approximated latent state vectors to provide a plurality of synthetic observations;
• and
• e) outputting the trained deep state space model;
• wherein the training data set includes a sequence of observation vectors describing one or more of:
• data demand at a plurality of network nodes, or attainable uplink or downlink rate relative to geographical position of a handset, or physical layer parameters including MIMO antenna configurations, OFDM subcarrier configuration, QAM index, channel coding modes, channel response between downlink and uplink, or a HARQ configuration.

An industrial machine or robot configured using the model, comprising:

• a controller configured, at least partially, using a deep state space model, the deep state space model including a generative model and a multi-modal inference model, wherein the generative model includes a transition model configured to describe a change of a plurality of latent states, and an emission model configured to decode the plurality of latent states to provide a plurality of synthetic observations, the deep state space model being trained by:
• a) receiving a training data set including a sequence of observation vectors each obtained at an observation step;
• for each of a plurality of observation vectors in the sequence of observation vectors, iterating b), c) and d):
• b) inferring, using the multi-modal inference model, a current latent state of the generative model by mapping a current observation vector obtained at a current observation step of the sequence of observation vectors to obtain a probability distribution of the current latent state,
• c) constructing, using the multi-modal inference model, a posterior approximation of the current latent state as a mixture density network, to yield a plurality of approximated latent state vectors,
• d) decoding, using the emission model, the plurality of approximated latent state vectors to provide a plurality of synthetic observations;
• and
• e) outputting the trained deep state space model;
• wherein the training data set includes a sequence of observation vectors describing one or more of:
• position of a portion of the machine or robot, or an operating temperature, or a vibration measure, or a sound or video measurement.