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20 Feb 2018: In dialogue management, the following kernelhas been successfully used:. k((b,a),(b′,a′)) = δ(a,a′) klin(b,b′). ... k((b,a,w),(b′,a′,w′)). = δ(a,a′) (klin(b,b. ′) klin(w,w′)). (9). 1A similar type of kernel extension has been

20 Feb 2018: k(, )is factored into separate kernels over the belief state and ac-tion space kB(b,b′)kA(a,a′). ... kB(b,b′) =. h. 〈bh,b′h〉, (6). where bh is the probability distribution encoded in the hth hid-den node.

20 Feb 2018: Based on this input, at every dialogue turn, a distributionof possible dialogue states called the belief state, an element of be-lief space b B, is estimated. ... kB(b,b′) =. h. 〈bh,b′h〉 (6). where bh is the probability distribution encoded in

20 Feb 2018: Based on this input, at every dialogue turn, a distributionof possible dialogue states called the belief state, an element of be-lief space b B, is estimated. ... kB(b,b′) =. h. 〈bh,b′h〉 (6). where bh is the probability distribution encoded in

20 Feb 2018: Based on this input, at every di-alogue turn, a distribution of possible dialogue states calledthe belief state, an element of belief space b B, is esti-mated. ... kB(b,b′) =. h. 〈bh,b′h〉 (8). where bh is the probability distribution encoded in

20 Feb 2018: u, sd, am)| {z }dialog model. P (p′|p)b(p, sd)| {z }belief refinement. ... m a. b. b. Summary Space. Fig. 3. Overview of Prototype HIS Dialog Manager.

20 Feb 2018: It takes values b B, where Bis a continuous space of dimensionality |S|, namely [0, 1]|S|. ... kB(b,b′) =. k. 〈bk,b′k〉, (15). where bk is the probability distribution encoded in the kth hiddennode.

20 Feb 2018: P(s′|s,a) =P(m′|a)P(l′|l,m,m′,u,u′)P(b′|b,m,m′,u,u′)P(c′|c,m,m′,u,u′) ... 0.8. 1.0. Polic. y speaksilentbackchannel. (b) Overlap. 0.0 0.2 0.4 0.6 0.8 1.0Time (sec).

20 Feb 2018: b′ = softmax([h g]{B}). where B is a parameter of the RNN. ... 5. 0. 5. 10. Ave. rage. rew. ard. RNNBNBN (constrained). (b) 30% error rate.

20 Feb 2018: where the kernel k(, ) is factored into separatekernels over the belief state and action spaceskC(b,b. ... kB(b,b′) =. h. 〈bh,b′h〉, (5). where bh is the probability distribution encodedin the hth hidden node.

20 Feb 2018: Q(b, a) = maxπ. Eπ. (. T. τ=t1. γτt1rτ |bt = b, at = a. ). , ... function,Q(b, a) GP (0, k((b, a), (b, a))) wherethe kernelk(, ) is factored into separate kernels over thesummary state and action spaceskB(b, b)kA(a, a).

13 Mar 2018: Oncc thu conrayonding pointr i n the left and thr r i b t tfnqt. ... 5 An implementation of a biprism-stereo camera! , I/. cL wcR (b) b x Y Fig.

20 Feb 2018: π(b) = F (π̄(f (b)), b) (6). Further explanation of the Summary POMDP methodcan be found in (Williams and Young, 2005). ... π̄(x) = arg maxāĀm. Q(F (ā, b), b) (7). 3 Summarised Q-learning.

13 Mar 2018: 6). µc =b P(c|b)b. b P(c|b)(7). σc =b P(c|b)(b µc)(b µc). ... al,. which would produce a P(w|B) as. P(w|B) b. P(w|c)P(c|B). (13).

20 Feb 2018: At each time-step,b isupdated asb′(s′) = η P (o′|s′, a). s P (s. ... b. best rest. b. b. CAM EDI LON. b. best rest.

20 Feb 2018: b. (b). a(1) a(3) a(2). z. Fig. 2. POMDP Value function representation: (a) shows exact rep-resentation; (b) shows grid-based representation. ... Map to Summary. Space. m a. b. b. Summary Space. Fig.

13 Mar 2018: be estimated, which are (A B ADC AFE %GIH. The second possibility is that voxel? ... B ) B " B B L! B )/ B " B L!

20 Feb 2018: Finally, the belief distribution b is updatedbased on o′ and am as follows:. ... m a. b. b. Summary Space. Figure 2: Overview of the HIS system dialogue cycle.