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# HW5 Example

For example, let us observe the state just for the slot "food" in a short dialogue.

Note: This is slightly refined/improved from what you've seen in the video. I've removed any dealings with bad ASR since you'll be working with textual inputs.

## Dialogue start

The belief state for food looks like this before the dialogue starts:

``````food: {None: 1.0}

``````

## Dialogue Turn 1

Let's assume that the system poses a starting question and the user replies:

``````Sys: Hi, how can I help?

Usr: I want Chines

``````

You can see that the user made a typo. The NLU isn't very confident about that, so you can get e.g. this probability distribution:

``````NLU: food=None: 0.8, food=Chinese: 0.2

``````

The state, given our update rule, is now simple -- all the probability was under None, so we can redistribute it according to the current values:

``````food: {None: 0.8, Chinese: 0.2}

``````

## Dialogue Turn 2:

The probability for Chinese is too low, so the system doesn't understand and the user needs to confirm in the 2nd state:

``````Sys: I'm sorry I didn't understand

Usr: Iwant Chinese

``````

Now the NLU is more confident. Since the user has made another typo, it's not completely sure. Let's assume we get this probability distribution from our NLU system:

``````NLU: food=Chinese: 0.7, food=Italian: 0.2, food=None: 0.1

``````

Now we have a 0.1 probability that food wasn't mentioned in this turn, so we take that amount to redistribute the previous probability. We add the non-null values from this turn, with their new probabilities. So this is how the computation looks like:

``````food: 0.1 x previous = {None: 0.08, Chinese: 0.02}

+ new: {Chinese: 0.7, Italian: 0.2}

``````

And this is the resulting state:

``````food: {None: 0.08, Chinese: 0.72, Italian: 0.2}

``````